Diffusion in Biological Systems

Drug diffusion is an essential mechanism for drug dispersion throughout biological systems. Diffusion is fundamental to the migration of agents in the body and, as we will see in Chapter 9, diffusion can be used as a reliable mechanism for drug delivery. The rate of diffusion (i.e., the diffusion coefficient) depends on the architecture of the diffusing molecule. In the previous chapter a hypothetical solute with a diffusion coefficient of 10-7 cm2/s was used to describe the kinetics of diffusional spread throughout a region. Therapeutic agents have a multitude of sizes and shapes and, hence, diffusion coefficients vary in ways that are not easily predictable. Variability in the properties of agents is not the only difficulty in predicting rates of diffusion. Biological tissues present diverse resistances to molecular diffusion. Resistance to diffusion also depends on architecture: tissue composition, structure, and homogeneity are important variables. This chapter explores the variation in diffusion coefficient for molecules of different size and structure in physiological environments. The first section reviews some of the most important methods used to measure diffusion coefficients, while subsequent sections describe experimental measurements in media of increasing complexity: water, membranes, cells, and tissues. Diffusion coefficients are usually measured by observing changes in solute concentration with time and/or position. In most situations, concentration changes are monitored in laboratory systems of simple geometry; equally simple models (such as the ones developed in Chapter 3) can then be used to determine the diffusion coefficient. However, in biological systems, diffusion almost always occurs in concert with other phenomena that also influence solute concentration, such as bulk motion of fluid or chemical reaction. Therefore, experimental conditions that isolate diffusion—by eliminating or reducing fluid flows, chemical reactions, or metabolism—are often employed. Certain agents are eliminated from a tissue so slowly that the rate of elimination is negligible compared to the rate of dispersion. These molecules can be used as “tracers” to probe mechanisms of dispersion in the tissue, provided that elimination is negligible during the period of measurement. Frequently used tracers include sucrose [1, 2], iodoantipyrene [3], inulin [1], and size-fractionated dextran [3, 4].

Pharmacokinetics of Drug Distribution

Pharmacology, the study of agents and their actions, can be divided into two branches. Pharmacodynamics is concerned with the effects of a drug on the body and, therefore, encompasses dose–response relationships as well as the molecular mechanisms of drug activity. Pharmacokinetics, on the other hand, is concerned with the effect of the body on the drug. Drug metabolism, transport, absorption, and elimination are components of pharmacokinetic analysis. Physiology influences the distribution of drugs within the body; overall distribution depends on rates of drug uptake, rates of distribution between tissue compartments, and rates of drug elimination or biotransformation. Each of these phenomena potentially involves aspects of drug diffusion, permeation through membranes, and fluid movement that were introduced in the previous sections. The goal of pharmacokinetics is synthesis of these isolated basic mechanisms into a functional unit; this goal is most often achieved by development of a mathematical model that incorporates descriptions of the uptake, distribution, and elimination of a drug in humans or animals. This model can then be used to predict the outcome of different dosage regimens on the time course of drug concentrations in tissues. The development of a complete pharmacokinetic model for any given drug is a substantial undertaking, since the fate of any compound introduced into a whole organism is influenced by a variety of factors, and is usually complicated—in ways that are difficult to predict—by the presence of disease. In this section, pharamacokinetics will be introduced by first considering the simplest situation: an agent is introduced into a single body compartment from which it is also eliminated. While quite sophisticated compartmental models can be developed from this basic construct, it is frequently difficult to relate model parameters (such as the volume of specific compartments or the rate of transfer between compartments) to physiological or anatomical parameters. To avoid this difficulty, physiological pharmacokinetic models are frequently employed; in these models, the kinetics of drug uptake, distribution, and elimination from local tissue sites are predicted by constructing anatomically and biochemically accurate models of the tissue environment.

Drug Transport by Fluid Motion

The rate of molecular movement by diffusion decreases dramatically with distance, and is generally inadequate for transport over distances greater than 100 μm. The movement of molecules over distances greater than 100 μm occurs in specialized compartments in the body: blood circulates through arteries and veins; interstitial fluid collects in lymphatic vessels before returning to the blood; cerebrospinal fluid (CSF) percolates through the central nervous system (CNS) in the brain ventricles and subarachnoid space. In these systems, molecules move primarily by bulk flow, or convection. Diffusive transport is driven by differences in concentration; convective transport is driven by differences in hydrostatic and osmotic pressure. This chapter introduces the principles of drug distribution by pressure-driven transport. The elaborate network of arteries, capillaries, and veins that carry blood throughout the body are described first in this chapter. Hydrostatic pressure within the blood vasculature drives fluid through the vessel wall (recall Equation 5-28) and into the extravascular space of tissues. Fluid flow through the interstitial space is not well understood, although the importance of interstitial flows in moving drug molecules through tissue is beginning to be appreciated. Engineering approaches for analyzing fluid flows in the interstitium are described in the second section of the chapter. Finally, the specialized systems for returning interstitial fluid to the blood are essential for clearance of molecules from the interstitial space; therefore, the chapter also provides a description of the dynamics of lymph flow in the periphery and CSF production and circulation in the brain. Our bodies appear, from the outside, to be solid masses that are slow to change, but, just beneath the surface, is a torrent of fluid motion. Blood moves at high velocity throughout the body within an interconnected and highly branched network of vessels. The cross-sectional area changes significantly along the network, and blood flow to the periphery emerges from the heart within a single vessel, which branches and rebranches to distribute blood to every tissue and organ.

Introduction

Humans have always attempted to improve their health by ingesting or administering drugs. Examples appear throughout written history, from every continent and culture. Noah produced alcohol [1] and Christ was offered a sedative to ease the pain of crucifixion [2]. The use of opium was described by Theophrastus in the third century B.C., the stimulating power of methylxanthines was exploited by ancient Arabian shepherds and priors, and the paralyzing properties of curare were recognized by native South Americans centuries before the arrival of Sir Walter Raleigh [3]. The chemotherapy of cancer, which many consider a modern development, has existed in some form for over 500 years [4]. Vaccination, the intentional exposure to pathogens, was used in China and India to prevent smallpox and other infections [5] centuries before the birth of either Jenner [6] or Pasteur [7]. Even during the 20th century, drug discovery frequently resulted from empiricism and happenstance. The anticancer effects of nitrogen mustard were realized during the development of chemical-warfare agents, and penicillin was discovered after the inadvertent contamination of a bacteriological plate. As technology advanced, particularly after 1970, methods of drug and vaccine production became more sophisticated and rational. In parallel with the rise of modern pharmaceutical technology and the explosive ascent of biotechnology, the cellular and molecular basis for the action of many drugs has been uncovered. Today, drug designers benefit from an accumulated base of scientific knowledge concerning, for example, the interactions between neurotransmitters and their receptors, the regulation of hormone secretion, and the sensitivity of tumor cells to specific kinds of chemicals. New technology and clearer biological insight have led to new classes of therapeutic and prophylactic agents. Consider some of the new products made available to patients in the United States over the last few years. A revolution in drug development is clearly upon us. Even more complex agents, such as chimeric antibodies, gene-based drugs, antisense oligonucleotides, and virus-like particles, are emerging as clinically viable entities. New clinical approaches involve cells as well as molecules; the introduction of genetically modified cells into humans has blurred the distinction between conventional pharmacology and transplantation.

Case Studies in Drug Delivery

This chapter illustrates the concepts presented throughout the book through the examination of three different clinical scenarios in which new methods for drug delivery are needed. Many agents cannot be administered orally because of poor absorption from the intestinal tract into the blood, yet they are rapidly eliminated once they enter the blood stream. Section 10.1 describes a controlled delivery system that produces prolonged levels of such an antiviral agent in the blood. The brain is protected from changes in blood chemistry by the blood-brain barrier; this natural defense mechanism makes drug delivery to the brain difficult. Section 10.2 describes one method for achieving prolonged concentrations of an active agent within a region of the brain. Finally, some agents are active on the skin or mucosal surfaces but must be present for long periods. Section 10.3 presents a method for prolonging the residence time of macromolecules on a mucosal surface. The three problems incorporate both aspects of the drug delivery challenge: design of methods or materials for introducing drugs into the body and optimization of the design to integrate the delivery system with the body’s natural mechanisms for distributing and eliminating foreign agents. Viral diseases are a significant cause of disability and death. Many deadly viral diseases—such as smallpox and polio—are now under control, due largely to the development of protective vaccines, but vaccines for certain viral illnesses have been difficult to develop. The development of an AIDS vaccine has been a priority among biomedical research efforts since the mid-1980s; tremendous energy and resources have been invested in this pursuit, but clinical progress towards a vaccine has been slow. On the other hand, antiviral therapies have had a significant impact on the clinical care of AIDS patients, particularly since multi-drug regimens targeting the retroviral reverse transcriptase and protease enzymes were developed in the late 1990s. However, many patients cannot tolerate aggressive antiviral therapy and development of drug-resistant viral strains is a persistent problem. Therefore, the search for alternative methods for blocking retroviral infections continues.

Controlled Drug Delivery Systems

In most forms of drug delivery, spatial localization and duration of drug concentration are constrained by organ physiology and metabolism. For example, drugs administered orally will distribute to tissues based on the principles of diffusion, permeation, and flow presented in Part II of this book. If the duration of therapy provided by a single administration is insufficient, the drug must be readministered. Localization of drug can be controlled by injection, but only within limited spatial constraints, and effectiveness after an injection is usually short-lived. Controlled-delivery systems offer an alternative approach to regulating both the duration and spatial localization of therapeutic agents. In controlled delivery, the active agent is combined with other (usually synthetic) components to produce a delivery system. Unlike drug modification, which results in new agents that are single molecules, or assemblies of a limited number of molecules, drug delivery systems are usually macroscopic. Like drug modification, controlled-delivery systems frequently involve combinations of active agents with inert polymeric materials. In this text, controlled-delivery systems are distinguished from “sustained-release” drug formulations. Sustained release is often achieved by mixing an active agent with excipients or binders that alter the agent’s rate of dissolution in the intestinal tract or adsorption from a local injection site. The distinction between sustained release (often achieved by drug formulation) and controlled delivery or controlled release is somewhat arbitrary. In our definition, controlled delivery systems must (1) include a component that can be engineered to regulate an essential characteristic (e.g., duration of release, rate of release, or targeting) and (2) have a duration of action longer than a day. Many polymeric materials are available for the development of drug delivery systems (see Appendix A). Non-degradable, hydrophobic polymers have been used the most extensively. Reservoir drug delivery devices, in which a liquid reservoir of drug is enclosed in a silicone elastomer tube, were first demonstrated to provide controlled release of small molecules several decades ago [1]. This discovery eventually led to clinically useful devices, including the Norplant® (Wyeth-Ayerst Laboratories) contraceptive delivery system, which provides reliable delivery of levonorgestrel for 5 years following subcutaneous implantation.

Drug Permeation through Biological Barriers

In multicellular organisms, thin lipid membranes serve as semipermeable barriers between aqueous compartments. The plasma membrane of the cell separates the cytoplasm from the extracellular space; endothelial cell membranes separate the blood within the vascular space from the rest of the tissue. Properties of the lipid membrane are critically important in regulating the movement of molecules between these aqueous spaces. While certain barrier properties of membranes can be attributed to the lipid components, accessory molecules within the cell membrane—particularly transport proteins and ion channels—control the rate of permeation of many solutes. Transport proteins permit the cell to regulate the composition of its intracellular environment in response to extracellular conditions. The relationship between membrane structure, membrane function, and cell physiology is an area of active, ongoing study. Our interest here is practical: what are the basic mechanisms of drug movement through membranes and how can one best predict the rate of permeation of an agent through a membrane barrier? To answer that question, this section presents rates of permeation measured in some common experimental systems and models of membrane permeation that can be used for prediction. The external surface of the plasma membrane carries a carbohydrate-rich coat called the glycocalyx; charged groups in the glycocalyx, which are provided principally by carbohydrates containing sialic acid, cause the surface to be negatively charged. On average, the plasma membrane of human cells contains, by mass, 50% protein, 45% lipid, and 5% carbohydrate. Given the mass ratio of protein to lipid is ~ 1 : 1, and assuming reasonable values for the average molecular weight and cross-sectional area for each type of molecule (50 × Mw,lipid = Mw,protein; Alipid = 50 Å2 and Aprotein = 1,000 Å2), the area fraction of protein on a typical membrane is ~ 33%. The lipid composition varies in membranes from different cells depending on the type of cell and its function. In addition, the outermost monolayer of lipids, called the outer leaflet, has a different lipid composition from the inner leaflet.

Drug Administration and Drug Effectiveness

There is some comfort to thinking of the human body as an elaborate bag of chemicals. Chemicals can be produced; chemicals can be added or replaced; chemicals are (sometimes) inexpensive. In fact, several decades ago, it was widely reported that the chemicals in the human body were worth about $1. Other investigators estimate the value at closer to $6 million (particularly if the chemicals are purchased from scientific suppliers). True dollar value aside, we often imagine that our bodies can be supplemented, mended, and improved through the addition of “missing” chemicals. Perhaps for this reason, the modern practice of healing usually involves medicine, an agent or elixir given as treatment. The new millennium finds us rich in the knowledge of agents; advanced in the art of harvesting or synthesizing remedies; steadfast in the belief that cancer, heart disease, and neurodegeneration will eventually yield to these potions. Our skill in making medicine is far-reaching. Today, it would be difficult to find the person who has not personally experienced the healing force of antibiotics, vaccines, or modern chemotherapy. Unfortunately, it would be equally difficult to find the person who has not endured the premature death of a friend or relative due to untreatable infection or cancer. So we continue to search for better therapeutics. Better medical treatments do not always require stronger medicine. The effectiveness of chemical agents depends on the method of administration, so treatments can often be improved by finding optimal drug formulations or delivery systems. For example, Banting and Best demonstrated control of diabetes by insulin injection in 1922. But early use of insulin was difficult: multiple daily injections were required and the effects were difficult to control. Insulin preparations have changed dramatically since that time; recombinant human insulin is now available in addition to highly purified insulin from animals. Today, the formulation of insulin is advanced: various formulations provide rapid or delayed action with long or short duration, so insulin therapy can be tailored to the needs of an individual. Intensive, individualized therapy decreases the long-term consequences of diabetes [1].

Drug Modification

Previous chapters present the characteristics of drug movement through the body. Diffusion is an essential mode of transport at the microscopic scale; concentration gradients drive a substantial fraction of the molecular movements within cells and the extracellular space. The confinement and regulated passage of molecules within compartments of a tissue or cell is also essential for function; membranes confine molecules to spatial locations and regulate transport between these isolated spaces (Chapter 5). Membranes frequently are the major obstacles to the entry or distribution of therapeutic compounds (Chapter 7). Therefore, much of the effort in drug design and drug delivery is devoted to overcoming these diffusional or membrane barriers. This chapter describes strategies for manipulating agents in order to increase their biological activity. The sections orbit a central assumption: i.e., agents can be modified to make analogous agents (analogs), which are chemically distinct from the original compound, but produce a similar biological effect. Nature uses a similar strategy, called “biotransformation” to assure elimination of many toxic compounds and drugs. Substantial chemical modification is often needed in order to impact physical properties that influence drug distribution such as stability or solubility; the challenge of drug modification is to identify chemical features that can be changed without sacrificing biological activity. Often, our understanding of the relationship between chemical structure and biological function for an agent is incomplete, making the rational production of analogs difficult. Drug modifications are frequently directed at altering properties that influence the concentration of the compound (i.e., its solubility), the duration of action (which is usually related to its stability in tissue), or the ability of drug molecules to move between compartments in tissues (which is often related to its permeability in membranes). A chemical modification can effect multiple properties, so these divisions are frequently not as distinct as the section headings suggest. Many agents are protected from degradation within tissues by binding. Binding provides a mechanism for sequestering an unstable or potent compound within a region of a tissue. Protective binding occurs frequently within the plasma and extracellular matrix (ECM); the complex molecular composition of these tissues provides many potential binding sites.

Diffusion and Drug Dispersion

Most biological processes occur in an environment that is predominantly water: a typical cell contains 70-85% water and the extracellular space of most tissues is 99%. Even the brain, with its complex arrangement of cells and myelinated processes, is ≈ 80% water. Drug molecules can be introduced into the body in a variety of ways; the effectiveness of drug therapy depends on the rate and extent to which drug molecules can move through tissue structures to reach their site of action. Since water serves as the primary milieu for life processes, it is essential to understand the factors that determine rates of molecular movement in aqueous environments. As we will see, rates of diffusive transport of molecules vary among biological tissues within an organism, even though the bulk composition of the tissues (i.e., their water content) may be similar. The section begins with the random walk, a useful model from statistical physics that provides insight into the kinetics of molecular diffusion. From this starting point, the fundamental relationship between diffusive flux and solute concentration, Fick’s law, is described and used to develop general mass-conservation equations. These conservation equations are essential for analysis of rates of solute transport in tissues. Molecules that are initially localized within an unstirred vessel will spread throughout the vessel, eventually becoming uniformly dispersed. This process, called diffusion, occurs by the random movement of individual molecules; molecular motion is generated by thermal energy.