In silico multiscale computational modelling of botulinum toxin a diffusion for glabellar wrinkle treatment:...

While botulinum neurotoxin A (BoNT/A) is a cornerstone in glabellar wrinkle treatment, inconsistencies in clinical outcomes often stem from formulation-dependent diffusion behaviour. Currently volumes recommendation per site lacks mechanistic justification, especially in anatomically confined regions like the glabella, where millimetric diffusion differences can produce significant adverse effects. A high-fidelity, multiscale in silico platform was developed, integrating quantum mechanical (TD-DFT) modelling of SV2-binding (ΔG_bind range: -9.2 to -11.7 kcal/mol), molecular dynamics-derived hydrodynamic radius (R_H: 9.4-11.2 nm), anisotropic finite element modelling of poroelastic muscle tissue, and agent-based receptor and immune kinetics. Simulations encompassed five formulations- AbobotulinumtoxinA (ABO), DaxibotulinumtoxinA (DAXI), IncobotulinumtoxinA (INCO), OnabotulinumtoxinA (ONA), and PrabotulinumtoxinA (PRABO)-across injection volumes from 0.025 to 0.1 mL, at fixed toxin unit dosing, within anatomically realistic glabellar meshes (n = 10,000 synthetic patient variants). Diffusion profiles varied significantly by formulation. ABO showed the largest Reff (1.64 ± 0.14 cm) and E_off, while PRABO and ONA remained spatially constrained (Reff = 0.96 ± 0.07 cm and 1.13 ± 0.08 cm, respectively). Increasing injection volume from 0.025 to 0.1 mL caused a 2.2-fold rise in E_off and a 36-49 % increase in off-target V_IC50 across formulations. Optimal containment was formulation-specific: PRABO and ONA achieved ≥95 % V_IC90 coverage with <10 % V_IC50 spillover at 0.025-0.035 mL; INCO and DAXI required 0.035-0.05 mL; ABO balanced broader coverage with acceptable diffusion at 0.04-0.045 mL. Agent-based models revealed 78 % receptor saturation at 0.025 mL versus 56 % at 0.1 mL, with immune clearance rates up to 42 % higher at high volumes due to increased perivascular redistribution. Volume emerged as the dominant spread driver (Sobol S₁ = 0.48), followed by hydrodynamic radius (S₁ = 0.35) and macrophage density (S₁ = 0.28); interaction terms were negligible (S_T - S₁ < 0.05). This study provides the first in-silico quantitative, multiscale evidence that reducing BoNT/A reconstitution volume to ≤0.045 mL/site significantly enhances target localization while minimizing off-target effects. Contrary to prevailing clinical heuristics, dilution amplifies mechanical spread and immune clearance risk.