Pharmaceutics 1 - Diffusion 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  17/11/2024 Pharmaceutics 1 Drug Release and Dissolution Prof. Rania Hamed Prof. Suhair Sunoqrot 2024/2025 Drug Release and Dissolution Drug release is the process by which a drug leaves a drug product and is subjected to absorption, distribution, metabolism, and excretion, eventually becoming available for pharmacologic action Dissolution is the process by which drug molecules are liberated from a solid phase (e.g. tablet) and enter into a solution phase Dissolution is an important process in the pharmaceutical sciences because only drugs in solution can be absorbed, distributed, metabolized, excreted, or exert pharmacologic action 1  17/11/2024 Dissolution Testing of Drug Products In vitro release tests are conducted on: – Solid oral dosage forms – Rectal dosage forms such as suppositories – Pulmonary (lung delivery) dosage forms – Modified-release dosage forms – Semisolid products (ointments, creams, and transdermal products) Terminology Drug Product: – A finished dosage form (tablet, capsule) that contains a drug substance Drug substance: – An active ingredient (active pharmaceutical ingredient: API) that is intended to exhibit pharmacologic activity Immediate Release: – Allows the drug to dissolve in the gastrointestinal contents with no intention of delaying or prolonging the dissolution or absorption of the drug 2  17/11/2024 Terminology Modified-Release Dosage Forms: – Dosage forms whose drug release characteristics of time course and/or location are chosen to accomplish therapeutic or convenience objectives not offered by conventional dosage forms. These include both delayed- and extended-release drug products Extended Release: – Formulated to make the drug available over an extended period after ingestion. This allows a reduction in dosing frequency compared to a drug presented as a conventional dosage form (e.g., as a solution or an immediate-release dosage form) Terminology Enteric Coated (delayed-release) dosage forms: – Intended to delay the release of the drug (or drugs) until the dosage form has passed through the stomach In Vitro-In Vivo Correlation (IVIVC): – A predictive mathematical model describing the relationship between an in vitro property of an oral dosage form (usually the rate or extent of drug dissolution or release) and a relevant in vivo response (plasma drug concentration or amount of drug absorbed) 3  17/11/2024 Drug Release Basics Drug release is largely based on diffusion Drug dissolution and release patterns fall into two groups: zero- and first-order release Zero-order release is achieved from non-disintegrating dosage forms such as topical or transdermal delivery systems, implantable depot systems, or oral controlled- release delivery systems Zero order means constant drug release from a drug delivery device “Constant”: the same amount of drug is released per unit time Donor Receptor Compartment Compartment Cd C1 Cd h High concentration of diffusant C2 Cr Cr molecules h Thickness of membrane 4  17/11/2024 Zero-order and First-order Release Kinetics Drug release here follows zero order kinetics which can be presented by the following equation: dM = PSCd dt Steady state (Zero order) Slope= PSCd This behavior is presented in the straight line presented in this figure First order If the excess solid in the dosage form is depleted, the (Cd) decreases (falls exponentially) as the drug diffuses out of the system (First order release). PSt log Cd = log Cdo − 2.0303Vd Zero-order and First-order Release Kinetics PSt log Cd = log Cdo − 2.0303Vd First order release Steady state Amount Diffused So diffusion controlled release in leads here to zero order release kinetics but would end up with first order kinetics after the depletion of excess drug in the reservoir Time 5  17/11/2024 The Higuchi Model Higuchi developed a theoretical model for studying the release of water-soluble and poorly-soluble drugs from polymeric matrices Let us consider a powdered drug homogeneously dispersed throughout the matrix of an erodible tablet In this case, the drug is dissolved in the polymer matrix and diffuses out from the surface of the device As the drug is released, the distance for diffusion increases with time The Higuchi Model The boundary that forms between the drug and the empty matrix recedes into the tablet as the drug is eluted Thus, the thickness of the empty matrix (dh) through which the drug diffuses increases with time 6  17/11/2024 The Higuchi Model As the drug is released, the boundary that forms between the drug and empty matrix recedes into the tablet and the distance for diffusion becomes increasingly greater. Therefore, drug release will be faster in the initial stages and become slower later as the remaining drug molecules should cross longer distances than the first drug molecules. The release in these systems is best described by Higuchi. The final form of the equation is known as the Higuchi equation. It shows a linear relationship between M and t1/2 M M t t Drug Release and Dissolution Process 1. When a tablet is introduced into a beaker of water or into the gastrointestinal tract, the drug begins to pass into solution from the intact solid 2. The solid matrix starts to disintegrate into granules 3. These granules deaggregate into fine particles 4. Fine particles dissolve into solution for absorption Disintegration, deaggregation, and dissolution may occur simultaneously with the release of a drug from the intact tablet 7  17/11/2024 Drug Release and Dissolution Process Drug Release and Dissolution Process Tablet undergoing Dry tablet dissolution Eroded tablet 8  17/11/2024 Drug Release and Dissolution Process The release of drug from a tablet for systemic absorption depends on: 1. The rate of disintegration of the dosage forms 2. The rate of deaggregation of the granules 3. Dissolution rate of the fine particles Dissolution is the rate-limiting step in the absorption of drugs with low solubility because it is often the slowest step in drug release Dissolution is a kinetic process → the rate of dissolution reflects the amount of drug dissolved over a given time period Dissolution rate: Noyes-Whitney Equation Dissolution rate: The rate at which a solid dissolves in a solvent was proposed in quantitative terms by Noyes and Whitney as follows: dM dC J= = -D dt.S dx – Where: M: mass of solute dissolved in time t dM/dt: mass rate of dissolution (mass/time) D: diffusion coefficient of the solute in the solution S: surface area of the exposed solid h: thickness of the diffusion layer Cs: solubility of the solid (concentration of a saturated solution at the surface of the solid) C: concentration of solute in the bulk solution at time t 9  17/11/2024 Noyes-Whitney Equation It is assumed that an aqueous diffusion layer or stagnant liquid film of thickness h exists at the solid- solution interface h represents a stationary layer of solvent in which the solute molecules exist in concentration from Cs to C Noyes-Whitney Equation At the solid surface-diffusion layer interface (x = 0), drug in the solid is in equilibrium with drug in the diffusion layer Across the diffusion layer (x = 0 to x = h), the gradient or change in concentration with distance is constant (slope of the straight line, (Cs – C)/h) Beyond h, mixing occurs in the solution, and the drug is found at a uniform concentration (C) throughout the bulk phase The thickness of the diffusion layer can change with mechanical agitation and stirring and this could affect the dissolution rate. 10  17/11/2024 Noyes-Whitney Equation The previous equation is similar to Fick’s first law of diffusion. The equation can be written in concentration forms as : dC (C − C ) = DS s dt Vh Where V is the volume of dissolution medium. When C