Drug Delivery and Mass Balance BIOE201-B

The concentration of the drug at the site of action, over time. Drug delivery is about the complex mechanisms to getting that concentration profile to happen. Delivery methods can be classified by the anatomical site they target (oral, injection, topical, transdermal, pulmonary, ophthalmic, rectal/vaginal, implantable depot device, etc.). Drug Delivery and Mass Balance

OralAdministration IntravenousInjection IntramuscularInjection SubcutaneousInjection GastrointestinalTract CirculatorySystem Tissues MetabolicSites Excretion

Even with controlled delivery side effects cannot be avoided Might cause severe side effects- spread over body Site specific delivery- active or passive targeting

RES Lungs Liver Spleen Reticuloendothelial System (RES) Site Specific Delivery

Enhanced permeability and retention (EPR) effect Disorganization of tumor vasculature Poor lymphatic drainage Passive Targeting of Particulate by EPR Mechanism

Ringsdorf’s Model Active Targeting

Various Drug Delivery System

Chemically-Controlled DDS

Major Classes of Matrix in DDS

Environmentally Responsive System

pH Responsive System

Absorption of drugs could vary within different administration routes 500 mg dose given – – intramuscularly – – orally **to the same subject on separate occasions Biological barriers greatly affect the extent of drug absorption

Absorption of drugs could vary within the same administration route

Drug Delivery System (DDS) Controlled delivery system Site specific delivery of drugs Toxicity Therapeutic Window No Therapeutic Effect

Time (min) Plasma concentration (mg/mL) Unsuccessful therapy Successful therapy

All drugs must diffuse through various barriers when administered to the body. Some drugs must diffuse through the skin, gastric mucosa, or some other barrier to gain access to the interior of the body. Parenteral drugs must diffuse through muscle, connective tissue, and so on, to get to the site of action. Intravenous drugs must diffuse from the blood to the site of action. Drugs must also diffuse through various barriers for metabolism and excretion. Laws governing diffusion are important to drug delivery systems

Fick’s law for diffusion, compartmental analysis, and the general use of mass conservation equations. The mass conservation equation: In – out + Generation - Consumption = Accumulation This equation, when properly replaced with mathematical terms, is used to describe transport everywhere. We can use simplified experiments and model fitting to calculate the value of drug diffusion constants, which can then be used to predict concentration profiles in relevant drug delivery scenarios.

Bioavailability is defined as a ratio of the areas under the curves (AUCs) of plasma concentration versus time. The AUC for intravenous injection is the standard, and any other delivery method is compared against that. Bioavailability and Area Under the Curve

Important Concepts Volume of distribution – –apparent volume into which a drug distributes in the body at equilibrium – –direct measure of the extent of distribution – –V = amount of drug in the body/Plasma drug concentration

Mathematical Modeling of Drug Disposition Single compartment Single compartment with absorption Two compartments Two compartments with absorption Physiological Models

These compartments don't usually correspond to actual bodily compartments, but they're still useful. The simplest case is the single‐compartment model. All the compartments are considered to be uniform and well‐mixed. Compartmental analysis In cases where the drug doesn't readily distribute to the whole body immediately, it's better to model things with more than one model. For example, using two of them:

Single Compartment Model Assumptions: – –Body one compartment characterized by a volume of distribution (V d ) – –Drug is confined to the plasma (small V) C, V d absorption elimination k, C t C/C 0

One-Compartment Model with Absorption Low absorption occurs Absorption is the rate- limiting step Slow absorption may represent drug entry through GI tract or leakage into circulation after SC injection Drugs require multiple doses to maintain drug concentration within therapeutic window t M/D 0 t

Two-Compartment Model Drug rapidly injected Drug distributed instantaneously throughout one compartment and slowly throughout second compartment Describes drug concentration in plasma injected IV C 1, V 1 C 2, V 2 k 2, C 2 k 12 k 21 k 1, C 1 Compartment 1 Compartment 2 tt Concentration after ingestion Concentration with slow absorption C/C 0

Diffusion occurs when individual molecules move within a substance, as the result of a concentration gradient or by random molecular motion. Molecular diffusion from a microscopic and macroscopic point of view. Initially, there are solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. Top: A single molecule moves around randomly. Middle: With more molecules, there is a clear trend where the solute fills the container more and more uniformly. Bottom: With an enormous number of solute molecules, randomness becomes undetectable: The solute appears to move smoothly and systematically from high- concentration areas to low-concentration areas. This smooth flow is described by Fick's laws. Fick’s Law

Fick’s first law relates to a steady-state flow J = dM/(S dt)= -DdC/dX J = Flux (in g/cm 2 s) M = material (in g) S = surface area (in cm 2 ) t = time (in s) D = diffusion coefficient (in cm 2 /s) C = concentration (in g/cm 3 ) X = distance of movement (in cm) units: g/cm^2*s Steady State Diffusion Fick’s second law relates to a change in concentration of drug with time, at any distance, or an unsteady state of flow. J= -D*(C1-C2)/h D = diffusion coefficient (in cm 2 /s) C = concentration (in g/cm 3 ) h = thickness of membrane (in cm) Non-Steady State Diffusion Partition Coefficient K=C1/Cd=C2/Cr K=[Drug]oil/[Drug]water determines concentration of drug in the membrane

29 A Versatile “Prodrug” Platform API= ACTIVE PHARMACEUTICS INGREDIENT SN-2

30µg/kg x 3 times (3, 6, 9 days) BiomaterialsBiomaterials, 2012, 33 (33), 8632– (33 Pan et. al. Nanomedicine (UK), 2012 Treated Un-treated AntiAngiogenic Therapy Pan et. al. Circulation. 2009, 120, S322. Comparison of MR Contrast Enhanced Images presented as 2D Slice and 3D Volume THERAPY NO THERAPY

Theranostic 2014