Lecture Slides 6 & 7 CH 8 Diffusion 2023 PDF

Diffusion — Molecules of solute tend to move from an area of high concentration to an area of lower concentration ¡ Establishes homogenous solution — Naturally occurring process ¡ Decrease in chemical potential/free energy Fick’s First Law of Diffusion (pp. 193-94) — Rate of diffusion proportio...

Diffusion — Molecules of solute tend to move from an area of high concentration to an area of lower concentration ¡ Establishes homogenous solution — Naturally occurring process ¡ Decrease in chemical potential/free energy Fick’s First Law of Diffusion (pp. 193-94) — Rate of diffusion proportionate to: ¡ Concentration gradient c = concentration of solute in g/mL of solution ÷ dc/dx = conc. gradient ÷ ¡ Cross-sectional area (A) ¡ Diffusion coefficient (D) is expressed as area per unit time dW/dt = -DA dc/dx ÷ ÷ ÷ ÷ ÷ dW/dt = number of grams transferred across boundary per second D = diffusion coefficient t = diffusion time “-"sign, so D will have a “+” value Dc/dx = conc. gradient The Diffusion Phenomena 5 — Fick’s 1st Law of Diffusion ¡ Diffusion occurs naturally because it is accompanied by a decrease in chemical potential or partial free energy change. ¡ Described by the following (J = flux) ÷J measures the amount of substance that will flow through a unit area during a unit time interval ¢ dw/dt = flux (J) Diffusion Coefficient — Equals the amount of solute diffusing across 1 cm2 in 1 second ¡ Then J = dw/dt = -Ddc/dx — Tendency of solute to diffuse ¡ Specific solvent – Specific temperature • Diffusion stops - when dc/dx*= 0 *conc. gradient The Diffusion Phenomena 7 — Driving force: free energy exchange ¡ Work done inorder to transfer one molecule across a distance (dx) — Counterforce to diffusion that allows the systems to reach homogeneity is frictional force exerted by viscosity (h) of the solution — Diffusion coefficient is a function of temperature/viscosity (T/h) and is related to solute radius. This Photo by Unknown author is licensed under CC BY-SA-NC. Sedimentation and Ultracentrifugation 8 • Distribution of solute molecules in space can be altered by added forces. • Sedimentation is simplest phenomenon which occurs when • • A solution is allowed to stand, unagitated • The force of gravity acts Ultracentrifugation • Greater affect than gravity: rotates at high speed (10,000 to 80,000 g) • Solute is forced to the outside by centrifugal force This Photo by Unknown author is licensed under CC BY. Ultracentrifugation 9 — Liquid rotates at an extremely high speed ¡ ¡ Distinction from centrifugation Solutes will move from center of liquid to outer layer Sedimentation & Diffusion Coefficients 10 — Diffusion (D) and sedimentation (S) are both dependent on the defined quantities ¡ Molecular weight of the solute and ¡ Densities of the solvent and solute ¡ Not dependent on viscosity and radius Fick’s 2nd Law of Diffusion 11 Explains the diffusion process in a given direction Results in changes in concentration along the direction of diffusion Involves mass transport through a cross-section Concentration change per time The diffusion distance is proportional to changes in the difference between concentrations at x and (x + dx). Fick’s 2nd Law of Diffusion 12 — Diffusion slows down when the concentration gradient decreases — Diffusion stops when C1 = C2 ¡ Establishes homogeneous solutions ¡ Non steady state flow This Photo by Unknown author is licensed under CC BY-SA. — Can establish a constant concentration gradient, experimentally ¡ Keep C1 at saturation ¡ Removing C2 constantly to create a sink condition Fick’s Laws of Diffusion (Summary) • First law: diffusion occurs according to a concentration gradient – Explains normal/natural diffusion – a solute will move across a concentration gradient from a region of high concentration to a region of lower concentration – Steady state flow • Second law: concentration gradient is required to maintain diffusion – Change in concentrations with time in a specific region is proportional to the change in the concentration gradient at that point in time – Predicts how diffusion will cause a concentration change with respect to time – Creates a sink condition that maintains flow – Non-steady state flow 13 Diffusion Methodologies/Theories 14 Diffusion Phenomena 2. Einstein’s random walk theory 3. Passive diffusion 1. Time-Distance Relationship • Einstein’s random walk theory – Can be used to determine the diffusion coefficient (D) – Two connected boxes containing solute – C1 > C2 – Diffusion occurs because of the concentration gradient – Diffusion is complete at time t • One-half C1 flows to box 2 & one-half C2 flows to box 1 t = time required for molecule to travel distance x 15 The Diffusion Phenomena 16 Membrane Diffusion and Permeability ¡ Determination of diffusion coefficient (D) is often experimentally measured in a two-chamber vessel separated by a porous membrane. ¡ System is calibrated with a compound whose D is known ÷ The area/thickness (A/h) of the diffusion layer can be determined ÷ D of the solute is determined based on flux (J) using the calibration value of A/h J = dw/dt = -Ddc/dx The Diffusion Phenomena 17 Membrane Diffusion and Permeability — Diffusion cell: Donor and receptor chambers ¡ ¡ ¡ ¡ Natural or synthetic membrane permeable to the solute Donor chamber contains the drug solution Receptor chamber contains the solvent Diffusion of the drug is monitored ÷ ÷ ÷ ÷ ÷ Function of time Constant temperature Constant stirring Drug concentrations in both chambers are sampled at specific time intervals Diffusion continues as long a diffusion layer exists (Fick’s Law) Passive Diffusion • Mass transfer of molecules based on a concentration gradient • Diffusion monitored as function of time – Constant temperature and stirring – Samples are taken from both chambers and analyzed • Diffusion will occur as long as the diffusion layer (h) is maintained – h = membrane thickness – Donor conc. decreases and receptor conc. increases with time – Rate of diffusion decreases with time • becomes zero when C1 =C2 18 The Diffusion Phenomena 19 — Sink Conditions and Kinetics ¡ Sink conditions implies that drug in the receptor chamber is constantly removed and the solvent (sample volume) is replaced. ¡ Goal is to drive concentration gradient to a constant ÷ ÷ ¡ Most closely mimics in vivo conditions. Steady state or quasi stationary condition is possible Basis of Fick’s Second Law of Diffusion Dissolution 20 — Theory of Dissolution ¡ Drug goes in solution under constant mixing ÷ Drug molecules at particle surface dissolve Diffusion layer established ¡ Concentration gradient established ¡ Ct < Cs ¡ ÷ Solubility is driven ¢ bulk solution will have an initial concentration of zero and a concentration at time t, Ct which is lower than Cs (solubility of the drug) Dissolution A kinetic process of solid (particles) going into solution Dissolution from solid dosage form (not solutions) • In vivo process is vital in determining bioavailability of a drug • In vitro tests are used to gain knowledge of the in vivo process Testing required for drug quality control Most important QC test for many pharmaceutical preps Wetting and Drug Release 22 — The release of drug from a solid dosage form consists of the following steps: 1) 2) 3) 4) 5) Wetting of solid dosage form ÷ Adhesive force between the solid and liquid forms ÷ Liquid film forms around the solid particle Penetration of the solvent into the formulation ÷ Important to the wetting process ÷ Hydrophobic additives (excipients) will reduce the rate of penetration and slow down disaggregation process Swelling process ÷ Additives can enhance, ex. cornstarch Disintegration and disaggregation ÷ Allows the dissolution process to began Dissolution ÷ Solubilizing the individual drug particles Dissolution Tests 23 Dissolution Methods ¡ ¡ ¡ Carried out by simulating in vivo sink condition constant replacing of the dissolution medium ÷ Solute conc. does not reach more than 10-15% of its maximum solubility ÷ The initial rate of dissolution is not affected by the concentration gradient Protocols described by USP in individual monographs for caps and tabs and specifies the apparatuses ÷ Apparatus 1: basket method Apparatus 2: paddle method Apparatus 3: reciprocating cylinder ÷ Apparatus 4: Flow-through cell ÷ ÷ Dissolution Dissolution rate studies ¡ ¡ Primary objective: assessment of oral drug absorption Physiological conditions ÷The volume of intestinal fluids ≅ 600 mL ¢ Depends on the volume of co-administered fluids ¢ Secretion of water flux across the gut wall Biopharmaceutical classification system (BCS) ¢ Utilizes 250mL of dissolution fluid (?) Dissolution Reported physiological conditions in GI tract after ingesting 250 mL • Stomach pH: 1.2 -7.4 (median = 1.7); fasting 6.4 • Intestines • Duodenum pH: 6.2-7.0 • Jejunum pH: 6.8 Dissolution Testing requires the use of simulated intestinal fluids. ÷ Most widely studied are the “fasting state” simulation intestinal fluid (FaSSIF) and the “fed state” simulated intestinal fluid (FeSSIF). 26 Factors Influencing Dissolution Rate 1. Diffusion Layer (h)Thickness ¡ thickness decreases over time ÷ ÷ ÷ Produces an increase in the intrinsic dissolution rate Time-dependent reduction in particle size and radius Follows 1st order kinetics h = 2r/Sh r = radius of spherical particle Sh* = Sherwood number = 2+ 0.6Re1/2Sc1/3 (ratio of the convective mass transfer to the rate of diffusive mass transfer) Re* = Reynolds number (ratio of the inert forces and viscous forces) *dimensionless numbers 27 Factors Influencing Dissolution Rate 2. Agitation: rotational — Low rpm: passive flow — Promotes dissolution of coarse particles or disintegration of formulation and granules — Dissolution rate depends on the way solid particles are scatter over the bottom of the vessels — Neither the solid nor the solution should move to the top of the system — Results in layers of solutions with different concentrations Factors Influencing Dissolution Rate Agitation: rotational (cont’d) ¡ Very high rpm Ø Produces turbulent flow Ø Centrifugal force of the rotating solution force particles upward and outward Ø Increase in agitation increases the dissolution rate constant An inverse relationship between agitation strength and the diffusion layer thickness ¡ Human intestines = 10-30 rpm using the scale paddle method ¡ Factors Influencing Dissolution Rate 3. pH § Fed state, pH ~6.4 § Fasting state, pH varies 1.2 -7.4 § After administration of 250 mL of water § Buffers can be used to adjust the pH • Add to formulation design Factors Influencing Dissolution Rate 4. Solubility and dissolution of weak electrolytes and salts. ¡ Weakly basic drugs: maximum solubility if pH < pKa Additional Factors Influencing Dissolution Rate Excipients in drug formulation can increase or decrease the aqueous solubility of drugs ÷ ÷ ÷ Lactose and starch may increase the dissolution of hydrophobic drugs in solid formulations Lubricants (ex. stearic acid and magnesium stearate) can decrease the dissolution of drugs ¢ Forms a hydrophobic layer that prevents interfacial interaction with water Surfactants: can increase dissolution rate ¢ facilitates the wetting process 32 Additional Factors Influencing Dissolution Rate Bile salts: bile acids and phospholipids (ratio = 4:1) ÷ Can form micelles (an aggregate of molecules) ¢ Diffusion of aggregates (micelles) is slower ÷ Solubility of lipophilic drugs are enhanced ÷ May increase the dissolution rate of poorly water-soluble drugs Additional Factors Influencing Dissolution Rate Particle size and surface area v Direct relationship v Surface area does not remain constant v Micronization of particles increase dissolution rate and oral absorption • Nernst-Brunner Equation Additional Factors Influencing Dissolution Rate Solid state properties v Polymorphism: one crystalline form maybe more soluble than another v Hydration: increases solubility v Physical form: powders verse crystals v Salts of weak acids and bases ü more soluble than the drugs themselves ü Can be used to increase dissolution and absorption September 7, 2023 Major factors that can affect drug dissolution rates in the GI tract pH • stomach • Fasting, 250mL of water: 1.2- to 7.4 (median 1.7) • Fed state: ~ 6.4 • small intestine • Fasting: 6.2-7.0 (duodenum) and 6.8 (jejunum) Buffer capacity (intestine) • main buffer is bicarbonate system • Fasting ~6.7 mM Surfactant concentrations in the intestinal fluid • Bile salts: • Fasting ~3 mM • Fed state ~5-15 mM • Bile salt/phospholipids ratio ~4:1 Commercially Available Permeability and Oral Drug Absorption — Multilayer diffusion ¡ Unstirred water layers (UWL) may exist on both sides of the membrane ÷ Thickness of the static layer can reach 15002000µm. ¢ ÷ Exists in the GI system adjacent to the intestinal membrane (30 – 100 µm thick). Effects absorption of drugs across biological membrane 39 Permeability and Oral Drug Absorption — 800 cm2 of intestinal surface area needed for sufficient oral absorption — Can be membrane-controlled or solubility- controlled. — Experimentally measured by a variety of systems. ÷ Most common = Caco*2 monolayer — Compounds with poor solubility generally have , high membrane permeability. *heterogeneous human epithelial colorectal adenocarcinoma cells 40 Permeability and Oral Drug Absorption — Intestinal Permeability ¡ The intestine has a high surface area making it ideal for oral drug absorption. ¡ Intestinal permeability, also known as effective permeability (Peff) is 10-4 cm/s. ¡ In vivo, drug is constantly removed from the intestinal membrane by blood flow 41 Permeability and Oral Drug Absorption Oral Absorption Profiles — Relative to Biopharmaceutical Classification System (BCS) rating ¡ Permeability ÷ Absorption largely based on combination of drug solubility and permeability. ÷ Highly permeable if intestinal absorption ≥ 90% 42 Permeability and Oral Drug Absorption Relative to Biopharmaceutical Classification System (BCS) rating — Solubility of IR products ¡ Rapidly dissolved ≥ 85% of labeled amount in 30 minutes ÷ ÷ Apparatus 1 @ 100 rpm or Apparatus 2 @ 50 rpm ¢ 900 mL or less as designated in USP Permeability and Oral Drug Absorption 44 BCS Classification Solubility Permeability I High High II Low High III High Low IV Low Low Permeability and Oral Drug Absorption — Class I (high solubility-high permeability) • Substances may qualify for waiver of in vivo bioavailability and bioequivalence studies — Class II (low solubility-high permeability) • Absorption is dissolution-limited • Percentage of drug absorbed is increased by increasing the dose amount and reducing particle size Permeability and Oral Drug Absorption — Class III (high solubility-low permeability) • Absorption is permeability-limited • An increase in dose increases the percentage of drug dose absorbed • Particle size reduction will not affect drug absorption Permeability and Oral Drug Absorption — Class IV (low solubility-low permeability) • Absorption is solubility and permeability limited • Increase in dose may increase the absorbed amount, if dissolution rate is slow • Particle size reduction may increase dissolution rate but not the absorbed amount Permeability and Oral Drug Absorption Simulation of Oral Absorption ¡ Can include dissolution testing, cell culture models, and computer modeling ¡ Oral absorption is a kinetic process ¡ Transit time is an important factor that determines drug absorption ÷ GI transient time in humans, fasting state ¢ Stomach = 12 minutes ¢ Intestines = 3 – 4 hours 48 FDA Waiver FDA guidance on securing a waiver of in vivo bioavailability and bioequivalence studies — IR solid oral dosage forms ¡ Highly soluble strength is soluble (≥ 90%) in 250 mL or less of aqueous media ÷ pH range of 1.2 – 6.8 ÷ highest Summary Chapter 8 — Most pharmaceutical products are for oral administration — Orally administered products are safe, efficient, easily accessible, and minimally uncomfortable to patients compared to other routes of administration — Solubility is a deciding factor for drug dissolution — Permeability describes the passive diffusion of drug through a membrane that impedes absorption