Pharmaceutics 1 Diffusion 2024/2025 PDF

17/11/2024 Pharmaceutics 1 Diffusion Prof. Rania Hamed Prof. Suhair Sunoqrot 2024/2025 What is diffusion? Diffusion is a process of mass transfer of individual molecules of a substance brough...

17/11/2024 Pharmaceutics 1 Diffusion Prof. Rania Hamed Prof. Suhair Sunoqrot 2024/2025 What is diffusion? Diffusion is a process of mass transfer of individual molecules of a substance brought about by random molecular motion and associated with a driving force such as a concentration gradient The mass transfer of a solvent (e.g. water) or a solute (e.g. drug) forms the basis for many important phenomena in the pharmaceutical sciences 1  17/11/2024 What is diffusion? Pharmaceutical applications of diffusion Diffusion phenomena applied to the pharmaceutical sciences include: 1. Release and dissolution of drugs from tablets, powders, and granules 2. Release of drugs from ointments and suppository bases 3. Permeation and distribution of drug molecules in living tissues 4. Passage of water vapor, gases, drugs, and additives through coatings and packaging materials 2  17/11/2024 How does diffusion occur? A solute or a solvent can traverse a physical or biological membrane by several ways: 1. Simple molecular permeation through nonporous media Depends on the solubility of the permeating molecules in the bulk membrane 2. Passage through solvent-filled pores of a membrane Influenced by the relative size of the penetrating molecules and the diameter and shape of the pores e.g. passage of a drug through human skin How does diffusion occur? (a) Homogeneous membrane without pores (b) Membrane with straight- through pores 3  17/11/2024 How does diffusion occur? A more realistic representation of a membrane is a matted arrangement of polymer strands with branching and intersecting channels Molecules may pass through the tortuous pores formed by the overlapping strands of polymer If they are too large they may dissolve in the polymer matrix and pass through by simple diffusion Fick's Laws of Diffusion These fundamental relationships govern diffusion processes in pharmaceutical systems Describe diffusion in terms of flux Flux (J) is defined as the amount (M) of material flowing through a unit cross section (S) of a barrier in unit time (t): Where: – The flux (J) is in g/cm2 sec – The mass (M) is in grams or moles – The barrier surface area (S) is in cm2 – The time (t) is in sec 4  17/11/2024 Fick's First Law of Diffusion The flux is also proportional to the concentration gradient, dC/dx: dM dC J= = -D dt.S dx Where: – D: diffusion coefficient (diffusivity) of the penetrant (diffusant) in cm2/sec – C: concentration of the penetrant in g/cm3 – x: the distance of movement perpendicular to the surface of the barrier (across the barrier) in cm – dc/dx: Concentration gradient which represents a change of concentration with a change in location (always negative value until reaching zero at equilibrium). Fick's First Law of Diffusion The negative sign of the equation signifies that diffusion occurs in the direction of decreasing concentration of diffusant Thus, J is always a positive quantity Diffusion will stop when the concentration gradient no longer exists (i.e. when dC/dx = 0). D is affected by concentration, temperature, pressure, solvent properties, and the chemical nature of the diffusant → it is not a proportionality constant 5  17/11/2024 Examples of Diffusion Coefficients Diffusivity (diffusion coefficient) is dependent on the solute’s molecular structure, temperature and medium through which diffusion occurs – Gas molecules diffuse rapidly through air and other gases – Diffusivity in liquids is smaller and in solids still smaller Fick's Second Law of Diffusion Fick’s first law examined mass diffusion across a unit area of a barrier in a unit time Fick’s second law examines the rate of change of diffusant concentration with time at a definite location (x) 6  17/11/2024 Fick's Second Law of Diffusion The diffusant concentration C in a particular volume element changes only as a result of net flow of diffusing molecules into or out of the region. A difference in concentration results from a difference in input and output Fick's Second Law of Diffusion The concentration of diffusant in the volume element changes with time (C/t) as the flux changes with distance (J/x): Differentiating the first law expression with respect to x: Fick's Second Law of Diffusion 7  17/11/2024 Steady state Diffusion ◼ Diffusion Cells: ◼ In a diffusion cell, two compartments are separated by a polymeric membrane. ◼ The diffusant is dissolved in a proper solvent and placed in one compartment while the solvent alone is placed in the other. ◼ The solution compartment is described as Donor Compartment because it is the source of the diffusant in the system while the solvent compartment is described as the Receptor Compartment. Steady state Diffusion Diffusion Cell Donor Receptor Compartment Compartment Diffusant Pure Solution solvent Membrane Flux in Flux out Flow of solvent to maintain sink condition 8  17/11/2024 Steady state Diffusion – As the diffusant passes through the membrane from the donor compartment (d) to the receptor compartment (r), the concentration in the donor compartment (Cd) will fall while the concentration in the receptor (Cr) will rise. – However, to mimic the biological systems; the solution in the receptor compartment is constantly removed and replaced with a fresh solvent to keep the concentration of the diffusant passing from the donor compartment at a low level. This is referred to as the Sink Condition. Steady state Diffusion Therefore, the concentration in the receptor compartment (Cr) is always maintained at very low levels because of the sink condition. In contrast, the concentration in the donor compartment (Cd) is kept very high or nearly constant (i.e. saturated solubility). This could be ensured by having a reservoir of precipitated or suspended drug for a long period of time. So drugs diffuse to the receptor compartment will be compensated by those dissolving from the suspended particles. Overall: Cd >> Cr. 9  17/11/2024 Steady state Diffusion dM dC J= = -D dt.S dx As both Cd and Cr are constant; concentration gradient (dc/dx) is constant (but not zero). (Note that the concentration in the two compartments is not the same). Furthermore, rate of diffusion (dM/dt) and consequently flux (J=dM/S. dt) are constant (but not zero). When the system has properties that are not changing with time, it is referred to be as in a steady state. Hence, the rate of change in concentration in the two compartments with time (dc/dt) will become zero. dc/dt = D*(d c/dx ) 2 2 Diffusion under such conditions is referred to as steady state diffusion. Steady state Diffusion dc/dt = D*(d2c/dx2) = 0 Since D is not equal to (0), then d2c/dx2 should be 0. Since d2c/dx2 is a second derivative, and is equal to (0) the first derivative dc/dx should be a constant. This means that the concentration gradient dc/dx across the membrane is constant (linear relationship between concentration c and distance or membrane thickness h) 10  17/11/2024 Steady state Diffusion Donor Receptor Compartment Compartment Cd C1 High constant concentration Cd Low constant C2 concentration Cr Cr 0 h Thickness of barrier dc/dx= c2-c1/h 4.6. Steady state Diffusion In such systems (diffusion cells), Fick’s first law may be written as: dM dC J= = -D dt.S dx dM ( C − C2 ) J= =D 1 S.dt h C1 and C2 are the concentrations within the membrane and are not easily measured. However they can be calculated using the partition coefficient (K) and the concentrations on the donor (Cd) and receptor (Cr) sides which can be easily measured 11  17/11/2024 Steady state Diffusion C1 C2 Considering : K = = Cd C r dM (C − C2 ) ( KCd − KCr ) J= =D 1 =D S.dt h h dM (C − C r ) = DSK d dt h Steady state Diffusion If the sink condition holds in the receptor compartment  Cd>>Cr  0 and Cr drops out of the equation which becomes Cr  Cd , , then : dM (C − C r ) (C ) = DSK d = DSK d dt h h The term DK/h is referred to as the Permeability Coefficient or Permeability (P) and has the units of linear velocity (cm/sec). The equation simplifies further to become dM / dt = PSCd dM = PSCd dt 12  17/11/2024 dM Steady state Diffusion = PSCd dt dM / dt = PSCd If Cd remains relatively constant throughout time, then diffusion follows zero order kinetics. k0 =PS Cd dM / dt = k0 M = k0t M = PS Cd t P can be obtained from the slope of a linear plot of M versus t. Amount Diffused Time Steady state Diffusion If Cd changes appreciably with time, then P can be obtained from the slope of log Cd versus t. dM dM / dt = PSCd = PSCd dt dCd/ dt = (PS/Vd) Cd log Cd = log Cd(0) - (PS/2.303Vd)t This eq. is first order (appreciable change in conc would happen at the last stages of drug release). As in this equation we used the conc. Term rather than M, we divided by Vd (volume of donor). First order PSt log Cd = log Cdo − 2.0303Vd 13  17/11/2024 Steady state Diffusion First order release PSt log Cd = log Cdo − Steady state 2.0303Vd Amount Diffused Time Examples of Diffusion and Permeability Coefficients 14  17/11/2024 Drug Absorption and Elimination Diffusion through biologic membranes is an essential step for drugs entering (absorption) or leaving (elimination) the body Mechanisms involved: – Transcellular diffusion: through the lipid bilayer of cells – Paracellular diffusion: through the spaces between adjacent cells – Membrane transporters (active transport or facilitated diffusion) – Cell surface receptors Gastrointestinal Absorption of Drugs Drugs pass through living membranes according to two main classes of transport, passive and carrier-mediated 1. Passive transfer involves a simple diffusion driven by a concentration gradient across the membrane – In the gastrointestinal tract, drugs travel from a region of high concentration to a region of low concentration in the systemic circulation – Sink conditions are maintained in the blood stream at all times 15  17/11/2024 Gastrointestinal Absorption of Drugs 2. Carrier-mediated transport – Active transport (requires an energy source) where the drug can proceed from regions of low concentration to regions of high concentration – Facilitated diffusion (does not depend on an energy source) where the drug is carried down the concentration gradient Gastrointestinal Absorption of Drugs Factors affecting the transport process: – Type of drug (weak acid/base, polarity) – The biologic compartments and membranes Drug absorption by diffusion is governed by: – State of drug ionization – Drug solubility – Drug concentration in the intestine – Membrane permeability 16  17/11/2024 Gastrointestinal Absorption of Drugs Biologic membranes are predominantly lipophilic, and drugs penetrate these barriers mainly in their molecular, undissociated form pH-partition hypothesis states that drugs are absorbed from the GIT by passive diffusion depending on the fraction of undissociated drug at the pH of the intestines This is under the assumption that the partition coefficient for the undissociated drug between the membranes and GI fluids is sufficiently large Henderson-Hasselbalch equation for: weak acids: weak bases: pH-Partition Hypothesis Transport of a drug by diffusion across the GI mucosa is governed by Fick's law: CrFirst Cd , , then : dM (C − C r ) (C ) = DSK d = DSK d dt h h – M: amount of drug in the GI compartment at time t – Dm: diffusion coefficient of the drug in the intestinal membrane – S: surface area of the membrane – K: partition coefficient between the membrane and the aqueous medium in the intestines – h: membrane thickness – Cg: concentration of the drug in the intestinal compartment at time t – Cp: concentration of the drug in the plasma compartment at time t 17  17/11/2024 pH-Partition Hypothesis Cg is sufficiently high and can be kept constant, and Cp ≅ 0 (sink conditions). Thus, the equation reduces to: Percutaneous Absorption Percutaneous penetration is the passage of the drug through the skin Percutaneous penetration of drugs involves three processes: 1. Dissolution of a drug in its vehicle 2. Diffusion of solubilized drug from the vehicle to the surface of the skin 3. Penetration of the drug through the layers of the skin, principally the stratum corneum 18  17/11/2024 Percutaneous Absorption The slowest step involves the passage through the stratum corneum (i.e. this is the rate limiting step for drug permeation through the skin) The stratum corneum is the outermost layer of the skin, and it is considered to be a dense homogenous film Percutaneous Absorption The drug can penetrate the skin by: A. Transcellular diffusion (predominant route) B. Diffusion through channels between cells C. Diffusion through sebaceous ducts D. Transfollicular diffusion E. Diffusion through sweat glands 19