The drug delivery from a diffusion based delivery system can be simulated using the transport of diluted species module in Comsol Multiphysics™. In order to predict how fast the drug diffuses from the active layer to a dissolution vessel or a physiological body, the compartments of the drug delivery system have to be defined in Comsol Multiphysics™, each with their specific solubility and diffusivity parameters. Interaction between the compartments is incorporated in the model by defining fluxes between the compartments. In order to determine the permeability properties of the materials several methods have been described in literature. Most often flat films are used to determine the permeability properties.

C = drug solubility
C_s = drug saturation solubility
D = drug diffusivity

The in-vitro release rate in a dissolution vessel (under sink conditions) can be quite different from the in-vivo infusion rate in a human body. Once administered the drug diffuses out of the delivery system and diffuses via the interstitial fluid through the tissue membranes into the systemic circulation. Local saturation of the drug may hamper the infusion rate to the systemic circulation. In order to predict the infusion rate and drug plasma levels a 1-compartment model can be added to the simulation. In order to predict the drug plasma level after administration of the delivery system the pharmacokinetic parameters clearance, distribution volume and permeability have to be known. These can be determined by pharmacokinetic studies in animals. The plasma levels in the human body can be determined via allometric scaling.

C = drug solubility
C_s = drug saturation solubility
D = drug diffusivity
CL = clearance
V_d = distribution volume

In the next examples both infusion rate and plasma levels were simulated for:

• matrix based implant
• matrix based implant where only the outer layer is loaded with drug
• reservoir based implant

Matrix delivery system

The drug delivery from a matrix based implant was simulated using arbitrary information such as the molecular weight, drug solubility, diffusivity and pharmacokinetic properties. The thickness and length of the implant are respectively 2 mm and 20 mm. The implant contains 50 wt.% crystalline drug. In order to study the influence of the drug permeability over the tissue membranes on the infusion rate and plasma levels the permeability was varied.

Matrix based implant 50 wt.% drug	Schematic figure model

In the figure below the infusion rate and related plasma levels are depicted after administration of the matrix based implant. The blue line depicts the infusion rate calculated for a high permeability over the tissue membranes. Here the infusion rate is almost equal to the in vitro release rate (matrix release profile according to Higuchi).  It can be seen that the plasma levels decrease with decreasing permeability and a zero order release is obtained. At lower permeability the release is fully controlled by the tissue membranes.  It can also be seen that at a lower infusion rate the time to reach C_max increases.

infusion rate

plasma level

blue – high permeability
green – intermediate permeability
red – low permeability

Matrix delivery system (outer layer only)

The drug delivery from a matrix based implant was simulated using arbitrary information such as the molecular weight, drug solubility, diffusivity and pharmacokinetic properties.  The thickness and length of the implant are respectively 2 mm and 20 mm. In contrast to previous example only the outer layer (100 µm) was loaded with crystalline drug. In order to study the influence of the drug permeability over the tissue membranes on the infusion rate and plasma levels the permeability was varied.

Matrix based implant outer layer loaded	Schematic figure model

In the figure below the infusion rate and related plasma levels are depicted after administration of the matrix based implant. Again it can be seen that the plasma levels decrease with decreasing permeability and a zero order release is obtained. Once the drug becomes depleted in the outer layer of the implant the release rate decreases to zero. By adapting the thickness of the outer layer the time of drug delivery can be tuned to the desired duration. In this way no more drug is used than is needed.

infusion rate

plasma level

blue – high permeability
green – intermediate permeability
red – low permeability

Reservoir delivery system

The drug delivery from a reservoir based implant was simulated using arbitrary information such as the molecular weight, drug solubility, diffusivity and pharmacokinetic properties.  The thickness and length of the implant are respectively 2 mm and 20 mm. The thickness of the membrane and active layer are respectively 60 µm and 50 µm. In order to study the influence of the drug load on the duration of the implant the drug load was varied to 10 wt.%, 20 wt.% and 30 wt.% drug.

Reservoir  based implant	Schematic figure model

In the figure below the infusion rate and related plasma levels are depicted after administration of the matrix based implant. It can be seen that the duration of the implant increases with increasing drug load. Once the drug become depleted in the active layer of the implant the release rate decreases to zero. By adapting the drug load in the active layer the time of drug delivery can be tuned to the desired duration. Similar to previous example no more drug is used than is needed.

infusion rate

plasma level

blue – 10 wt.%
green – 20 wt.%
red – 30 wt.%