The Linear Theory Of Transdermal Transport Phenomenon

The linear theory of transdermal transport phenomenon is a concept that has been studied extensively in the field of pharmacology and drug delivery. It refers to the process by which drugs are delivered through the skin and into the bloodstream. This theory is based on the idea that the rate of drug transport is directly proportional to the concentration gradient of the drug across the skin.

The skin is the largest organ in the human body, and its primary function is to act as a barrier between the external environment and the internal organs. However, the skin is also permeable to certain molecules, including drugs. The ability of drugs to penetrate the skin depends on several factors, including the physicochemical properties of the drug, the condition of the skin, and the formulation of the drug. The linear theory of transdermal transport phenomenon is based on Fick's Law of Diffusion, which states that the rate of diffusion of a substance is proportional to the concentration gradient of the substance. In the case of transdermal drug delivery, this means that the rate of drug transport through the skin is proportional to the concentration gradient of the drug across the skin.

The concentration gradient of the drug across the skin is determined by the concentration of the drug in the formulation and the concentration of the drug in the bloodstream. The concentration of the drug in the formulation is typically higher than the concentration of the drug in the bloodstream, which creates a concentration gradient that drives the drug through the skin and into the bloodstream.

The rate of drug transport can be calculated using the following equation:

J = Kp (C1 - C2)

Where J is the rate of drug transport, Kp is the permeability coefficient of the skin, C1 is the concentration of the drug in the formulation, and C2 is the concentration of the drug in the bloodstream.

The permeability coefficient of the skin is a measure of the skin's ability to allow the drug to penetrate through it. The permeability coefficient depends on several factors, including the thickness of the skin, the lipid content of the skin, and the hydration state of the skin.

Why Transdermal Drug Transport ?

The transdermal drug release is a viable administration route for powerful, low molecular weight therapeutic agents, which has to be precise in their control of drug distribution. This strategy is specially recommended for many drugs that are difficult to be taken since they must be delivered slowly over a prolonged period to have a beneficial effect. However, there is still necessary to research in this field. For instance, the drug release modelling of biodegradable polymeric systems by encapsulation technology in textiles has not progressed much yet, due to its high complexity.

The topical administration shows far less problems than the transdermal one for the use of drug delivery system. However, transdermal administration has several interesting advantages over other systemic administration routes such as:

1. The reduction of first-pass drug degradation as the liver is initially bypassed.
2. The reduction of over dosage peaks that can appear in oral administration.
3. The existence of variable delivery conditions, typical of the gastrointestinal tract.

The dermis consists of tissue layers of mesenchymal origin. Finally, the inner layer is represented by subcutaneous tissue, which consists mainly of connective tissue.

Schematic representation of the transport processes involved in drug release from the formulation up to its uptake through the dermal capillaries.

Transdermal Transport Approaches :

Numerous quantitative approaches to transdermal transport phenomena have been advanced in the past, many of which may be classified according to the following categories:

1. Circuit model
2. Macroscale models
3. Parametric models

Macroscale Laws :

This image shows the best cross-sectional diagram of the epidermis of mammalian skin. The epidermis is characterized by three equal layers: the thin stratum corneum, the active substance and the papillary layer of the epidermis. The second layer is rich in capillaries and represents, at least in the context of this article, the last term of the solute species that can originate from the skin surface (its surface is always n). This application creates a mass of fluid (ie, water velocity V), stretch (J), and load (J) across the epidermal layer to the papillary dermis. 

Transdermal transport of fluid mass may be described by the generalized Darcy’s law equation ,

where ,V is the volume-average (or so-called “seepage”) velocity vector, ,uf is the viscosity of the flowing fluid, K the hydraulic permeability, and KE the electroosmotic permeability.

Application of the Macroscale Laws:

Transdermal Drug Delivery-

Transdermal drug delivery offers a compelling physical example of the above macrotransport processes. In the simplest case of drug delivery by passive diffusion, a concentration-gradient field (VC) is applied across the skin. This field results in a net macroscale flux (J) of solute (i.e., drug) across the epidermis. Thus, the drug enters the papillary dermal layer, where it may be taken up by the bloodstream.

Frequently, however, the magnitude of solute flux created solely by the concentration-gradient field (VC) is far too small for practical drug delivery purposes. Thus, additional driving forces may be applied. Enhanced deg delivery schemes involving application of an electric field-(E) (typically in addition to a-concentration-gradient field, VC), give rise-to a solute flux, J, that is accompanied by a flow of current J,, across the skin, as well as a finite water velocity, t, the latter owing to the indigenous negative charge bocne by skin at physiological pH.65 Pressure-gradient fields  may also be applied in the interests of enhancing drug delivery, as in sonophoretic.

Idealized Transport Pathway Formulas:

Intracellular/shunting pathways link the (a) macroscale (eg, -1 mm) conductivity of the skin to the generation of ion flux from the intra stratum corneum water pathway and parallel flow through sweat channels and the ring around the hair shaft. These three methods are medium-sized (ie., -50 pm) phase description. At this scale, the stratum corneum is seen as a homogeneous medium with anisotropic conductivity @ SC. Sweat ducts are in the form of cylinders penetrating the stratum corneum. It is shown below that sweat channels are connected to the dermis of the skin by joining the epidermal length scale (L) instead of the stratum corneum (H). (The same advice applies to our best hair root.) the hair shaft is also ideal as a cylinder, and in the cylindrical hair follicle, the annular space between the cuticle and the hair shaft is filled with an aqueous solution similar to the one occupying the sweat duct, at least in terms of its charge. The shunt can be considered conductive, & H. 

The intercellular/shunt route of transdermal transport. The macroscale level of description of the skin corresponds to the view of the skin sample in the diffusion cell of above Figure At the mesoscale level of description, the stratum corneum is revealed to be perforated by circular cylindrical sweat ducts and annular channels between hair shafts and follicles. At the microscale level, the stratum corneum consists of rectangular, nonconducting corneocyte cells  (presumed to possess a relatively infinite length in the direction perpendicular to the page) separated by rectilinear  lamellar layers. The lamellar layers  are found, at  the microscale level of description, to consist of parallel lipid and water layers Transport occurs either through the shunt (hair follicle and sweat duct) pathways or between the corneocyte cells via either the lipid or water layers.

The transcorneocyte route of transdermal  transport The macroscale level of description is  identical to that depicted in above Figure The mesoscale level of description characterizes the  stratum corneum as alternating  layers of lamellar and corneocyte phases. Each of these  phases possesses a substructure at the microscale level. The corneocyte  cells are depicted as perforated by circular cylindrical aqueous  pores through a nonconducting keratin environment. The lamellar regions consist of alternating lipid and water layers The lipid layers, at the sub microscale level of description, are shown to be perforated by circular cylindrical aqueous pores. Transport, according to this pathway, occurs through aqueous pores existing both in the corneocyte and lamellar layers.

Intercellular/Shunt Route: Summary of Results :

The transport coefficients K, PE, a, pp, U*, and D* corresponding to this route of transport are summarized below. Further discussion of these formulas is provided in the next section, where comparisons are made with experimental data. Effective Hydraulic Permeability-A finite effective hydraulic permeability of the skin may be attributed to the existence of three hydraulic pathways.

In general, effective permeability can be demonstrated as ,

The mean solute velocity may be regarded as being of the generic form ,

 Trans Corneocyte Route:

 Physical Description -This route of transport has not been considered seriously in the literature as offering a viable transdermal pathway for charge, fluid-mass, and/or solute transport.

This is partly due to the fact that translaminar transport is required to allow substantial transport along the pathway (including transport through the keratinocyte membrane required for penetration into the keratinocyte), which is often also considered indirectly for the horizontal bilayer and discrete transport. However, this may not be the case. The results show that small ions can enter the bilayer at a reasonable rate in the presence of electricity. Additionally, in a subsequent paper, 4O provided evidence that the trans keratinocyte pathway may be a pathway for macromolecular transport, particularly in "high-use, pulsed electric field" conditions. In general, the trans keratinocyte method is useful, at least to the extent that the method is accessible .

Conclusion :

The theory outlined here provides a mathematically rigorous, independent environment for studying transdermal transport events based on respected principles such as intercellular predation and the fundamentals in the preparation of trans keratinocyte transport. Two new theoretical aspects of transdermal transport deserve special attention in future experiments, and they affect (i) the hydraulic permeability of the skin and (ii) the contribution of convective diffusion to the efficient diffusion of solutes. To our knowledge, experimental measurements of skin permeability K have not been reported. Such a measurement would require measuring the flow of the identified transdermal drop across the stratum corneum. The use of this theory to predict rates of negative charge or macromolecular transport often requires knowledge of the dispersion coefficients as well as the various hydrodynamic inhibition coefficients.

One of the main strengths of the current theory is that it can be applied to very complex geometric patterns. For example, the application of spatial periodicity paradigms, such as those described in the Supplement, has been made in recent years to irregular and fractal cellular geometries, as discussed in detail from Alder. The drug mixture of fluids in the skin is thought to play an important role in transdermal drug delivery. Extending existing theories to include these effects is promising because the theory underlying macroscopic transport processes is often applied to chemical transport reactions.