Same volume, same dose, three geometries — how gyroid, cylinder, and torus printlets dissolve on different clocks
Dissolution science has long recognized that surface area governs release rate (the Noyes-Whitney equation makes this explicit), but conventional tableting offers only crude geometric control — round, oval, or caplet-shaped punches. Fused deposition and vat-photopolymerization 3D printing allow arbitrary internal and external architectures at equal total volume, turning shape itself into a rigorously testable formulation variable.
Compressed tableting is fundamentally a subtractive-adjacent, mold-based process: a die and two punches compress powder into whatever shape the tooling allows — almost always a simple convex solid (round, oval, capsule). Internal architecture (porosity, channels, cavities) is essentially unachievable because compression forces would collapse any internal void.
3D printing removes this constraint entirely. Fused deposition modeling (FDM) and vat photopolymerization (SLA/DLP) build the printlet as a sequence of independently defined 2D cross-sections, so:
• Internal lattices (gyroid, honeycomb, diamond) can be specified as freely as external contours • Non-convex external shapes (torus, hollow shell, multi-lobed) are trivial to slice and print • The same CAD/slicer pipeline used for infill-based dose titration (see companion module) can hold total volume and dose constant while systematically varying only shape — an experimental design impossible with compression tooling
This experimental control is what allows shape-dependent dissolution to be studied (and exploited) as cleanly as a formulation excipient study — with geometry playing the role normally reserved for polymer molecular weight or plasticizer content.
The Noyes-Whitney equation, dC/dt = (D·A/h)·(Cs − C), makes surface area (A) a first-order determinant of dissolution rate alongside diffusion coefficient and boundary layer thickness. Because 3D printing controls A independently of total volume, it directly manipulates the single geometric term in this century-old pharmaceutical kinetics equation.
For a matched total volume of ~200 mm³:
Solid cylinder: the reference minimum-surface geometry. A right cylinder of volume V has surface area minimized when height ≈ diameter; even at this optimum, a solid convex shape inherently has the lowest achievable SA:V ratio of any of the three designs — dissolution medium can only access the smooth outer envelope.
Torus (ring): introducing a central through-hole adds both an inner cylindrical surface and two additional annular end faces without changing total volume. This raises SA:V by roughly 40–50% over an equivalent solid cylinder, while the ring remains a fully dense, non-porous solid (no internal lattice) — useful when a formulator wants faster release than a solid cylinder but does not want the more complex, weaker gyroid internal architecture.
Gyroid lattice (triply periodic minimal surface, TPMS): at typical printable infill densities (20–40%), the interconnected internal channel network exposes far more wetted surface per unit volume than any convex external shape — a gyroid printlet at 200 mm³ external volume can present more than double the cylinder's surface area, because dissolution medium penetrates and wets internal channel walls throughout the entire structure, not just the outer boundary.
Because D (diffusion coefficient) and Cs (drug solubility) are formulation-fixed constants in this comparison, the surface area term A is doing all of the mechanistic work in separating the three release profiles.
A 2020 University College London/FabRx study comparing 3D-printed paracetamol printlets of matched dose and volume found t50 values of approximately 35 minutes for a high-surface-area gyroid geometry versus over 180 minutes for a solid cylinder — more than a 5-fold difference from shape alone.
Surface area alone does not fully determine release kinetics — the spatial pathway by which dissolution medium reaches the drug-polymer matrix, and whether that path shortens or lengthens as dissolution proceeds, differs qualitatively between the three geometries and produces distinct release-order signatures.
Solid cylinder: dissolution medium penetrates radially inward from the smooth outer surface. As the erosion front advances toward the core, the remaining unwetted cross-sectional area shrinks — for a purely diffusion-controlled matrix, this produces a declining release rate over time, consistent with Fickian (n≤0.45) kinetics and a classic Higuchi √t profile. The very core of the cylinder is the last and slowest region to be reached, creating a long dissolution "tail."
Torus: medium attacks from two fronts simultaneously — the outer circumference (as in the cylinder) and the inner bore surface, both advancing toward the mid-thickness of the ring wall. This halves the effective maximum diffusion path length compared with a solid cylinder of similar wall cross-section, meaningfully accelerating the later stages of release and reducing the dissolution tail, while keeping fabrication as a single fully dense print (no internal lattice fragility).
Gyroid lattice: because the TPMS channel network is already open to the exterior at essentially every point of the structure, dissolution medium reaches deep interior channel walls almost as quickly as it reaches the outer shell — ingress is not a slowly advancing 1D or 2D front but a near-simultaneous 3D wetting event throughout the accessible pore network. This produces the fastest overall release and the kinetics most likely to show an anomalous-to-Case-II signature (n approaching or exceeding 0.89), since polymer matrix erosion/relaxation at the many exposed internal channel walls contributes alongside diffusion.
| Product | Indication | Trial Design | Key Result |
|---|---|---|---|
| Solid Cylinder | Lowest SA:V (~0.42 mm⁻¹) | Radial diffusion front, shrinking active area, long core-release tail | Simple, robust, best for true sustained-release |
| Torus (Ring) | Intermediate SA:V (~0.63 mm⁻¹) | Bidirectional ingress (outer + inner bore), shortened max path length | Tunable mid-range release, fully dense/robust print |
| Gyroid Lattice | Highest SA:V (~0.95 mm⁻¹) | 3D interconnected channel wetting, near-simultaneous internal ingress | Fastest release, best for immediate-release printlets |
Visual comparison of dissolution curves is suggestive, but formal kinetic modeling is what makes shape-dependent release a defensible, quantitative CMC parameter — translating each geometry's release profile into a small set of numbers (k, n) that can be specified, controlled, and compared statistically across batches.
The Korsmeyer-Peppas release exponent n was originally derived for and is most rigorously applicable to simple geometries (thin films, cylinders, spheres), which makes it an especially natural tool for characterizing 3D-printed printlets whose exact geometry is known precisely from the CAD file — unlike compressed tablets, whose internal microstructure is not deterministically known.
For a cylindrical matrix, n≈0.45 marks the pure Fickian diffusion boundary; n≈0.89 marks pure Case-II (erosion/relaxation-controlled) transport; values between are "anomalous," reflecting a mixture of both mechanisms. Because the gyroid geometry exposes internal polymer surfaces directly to solvent throughout the structure, polymer chain relaxation and matrix erosion contribute proportionally more to overall release than in a solid cylinder — mechanistically explaining why gyroid printlets consistently fit higher n values than solid cylinders of the same formulation.
Regression practice: cumulative release data (percent released vs. time, typically sampled every 5–15 minutes over 2–4 hours in USP Apparatus II) are log-transformed (log(Mt/M∞) vs. log t) and fit by linear regression over the first 60% of release, per the standard applicability limit of the Korsmeyer-Peppas model. R² >0.98 is typically required before the fitted n is considered mechanistically interpretable rather than merely descriptive.
Because n and k are derived directly from a known, CAD-specified geometry rather than an empirically variable compressed microstructure, 3D-printed printlets offer an unusually clean experimental system for validating dissolution mechanism theory itself — several recent academic groups now use printed geometries specifically as reference standards for testing kinetic models.
The practical payoff of shape-dependent dissolution science is a new design freedom: a single drug-polymer system, once developed and characterized, can be deployed across an immediate-release-to-sustained-release spectrum purely by changing which CAD file is sliced and printed — with no new excipients, no new stability program, and no new API-polymer compatibility study.
A formulator developing a 3D-printed product line can now treat shape/infill architecture as an explicit, validated Critical Process Parameter (CPP) governing a Critical Quality Attribute (dissolution rate) — conceptually identical to how compression force is a CPP governing tablet hardness and disintegration in conventional manufacturing, but with far greater design flexibility because geometry is digitally specified rather than mechanically constrained by tooling.
Design space example: a single levetiracetam-HPMC printlet formulation could be specified to print as: • A high-infill/solid-cylinder variant for once-daily sustained-release dosing (t50 ≈ 180 min) • A gyroid, low-infill variant for immediate-release, rapid-onset dosing (t50 ≈ 35 min) • A torus, mid-infill variant for a twice-daily intermediate-release profile (t50 ≈ 90 min)
...all from the same qualified drug-loaded filament lot, the same API-polymer compatibility and stability data package, differentiated only by the sliced geometry file selected at print time. This has direct implications for the regulatory pathway discussed in the companion module on point-of-care 3D-printed medicine approval: a validated "volume-and-shape-to-release-profile" computational model, rather than per-product clinical bioequivalence studies, becomes central CMC evidence supporting the full family of geometries derived from one formulation.