Diffusion and Drug Dispersion

Drug Delivery ◽  
2001 ◽  
Author(s):  
W. Mark Saltzman
Keyword(s):  
Statistical Physics ◽  
Molecular Diffusion ◽  
Bulk Composition ◽  
Mass Conservation ◽  
Biological Tissues ◽  
Solute Concentration ◽  
Conservation Equations ◽  
Drug Molecules ◽  
Molecular Movement ◽  
Typical Cell

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.

Diffusion in Biological Systems

Drug Delivery ◽  
2001 ◽  
Author(s):  
W. Mark Saltzman
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Molecular Diffusion ◽  
Biological Systems ◽  
Biological Tissues ◽  
Solute Concentration ◽  
Diffusion Resistance ◽  
Experimental Conditions ◽  
Composition Structure ◽  
Reliable Mechanism

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].

Dynamic Model of Launching Process for Novel Gas Gun and its Validation

2015 ◽  
Author(s):  
Li Feng ◽  
Bai Yunshan ◽  
Zhu Yongqing
Keyword(s):  
Equation Of State ◽  
Dynamic Model ◽  
Mass Conservation ◽  
Gas Pressure ◽  
Second Law ◽  
Conservation Equations ◽  
Muzzle Velocity ◽  
Gas Gun ◽  
Valve Opening ◽  
Relationship Of

Launching process of gas gun involves valve opening, gas flowing, and bullet moving, etc, which is complex and difficult to describe clearly, and establishing an accurate dynamic model of the process is meaningful to gas gun design and analysis. The dynamic model of launching process for a novel gas gun is originally posted in this paper, which is described with a series of equations according to mass conservation equations, gas equation of state, Newton’s second law, relationship of movement and space. And the key parameters such as muzzle velocity, gas pressure, and time taken to open valve are calculated based on the dynamic model above-mentioned. Then, the bullet launching experiment was designed and implemented, and muzzle velocity of the bullet was measured. The deviation of the muzzle velocity calculated based on the dynamic model and the velocity measured in the experiment is less than 3 percents, which shows that the dynamic model established could describe the launching process of the gas gun accurately.

Drug Transport by Fluid Motion

Drug Delivery ◽  
2001 ◽  
Author(s):  
W. Mark Saltzman
Keyword(s):  
Drug Transport ◽  
Interstitial Fluid ◽  
Fluid Motion ◽  
Convective Transport ◽  
Interstitial Space ◽  
The Body ◽  
Cross Sectional ◽  
Drug Molecules ◽  
Molecular Movement ◽  
The Brain

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.

scholarly journals A New Model for Predicting Dynamic Surge Pressure in Gas and Drilling Mud Two-Phase Flow during Tripping Operations

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Xiangwei Kong ◽  
Yuanhua Lin ◽  
Yijie Qiu ◽  
Hongjun Zhu ◽  
Long Dong ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Drill Pipe ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Operating Speed ◽  
Drilling Mud ◽  
Two Phase ◽  
Influx Rate ◽  
Conservation Equations ◽  
Calculation Results

Investigation of surge pressure is of great significance to the circulation loss problem caused by unsteady operations in management pressure drilling (MPD) operations. With full consideration of the important factors such as wave velocity, gas influx rate, pressure, temperature, and well depth, a new surge pressure model has been proposed based on the mass conservation equations and the momentum conservation equations during MPD operations. The finite-difference method, the Newton-Raphson iterative method, and the fourth-order explicit Runge-Kutta method (R-K4) are adopted to solve the model. Calculation results indicate that the surge pressure has different values with respect to different drill pipe tripping speeds and well parameters. In general, the surge pressure tends to increase with the increases of drill pipe operating speed and with the decrease of gas influx rate and wellbore diameter. When the gas influx occurs, the surge pressure is weakened obviously. The surge pressure can cause a significant lag time if the gas influx occurs at bottomhole, and it is mainly affected by pressure wave velocity. The maximum surge pressure may occur before drill pipe reaches bottomhole, and the surge pressure is mainly affected by drill pipe operating speed and gas influx rate.

scholarly journals Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

Metals ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 889 ◽  
Author(s):  
Naseri ◽  
Larouche ◽  
Martinez ◽  
Breton ◽  
Massinon
Keyword(s):  
Mixed Mode ◽  
Analytical Modeling ◽  
Mass Conservation ◽  
Time Discretization ◽  
Solute Concentration ◽  
Conservation Equation ◽  
The Matrix ◽  
Numerical Solver ◽  
Interfacial Mobility ◽  
Discretization Procedure

In this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility of the precipitate. The dissolution model is developed by neglecting the transient term in the mass conservation equation, keeping the convective term. It is shown that such an approach yields the so-called reversed-growth approximation. A time discretization procedure is proposed to take into account the evolution of the solute concentration in the matrix as the phase transformation progresses. The model is applied to calculate the evolution of the radius of spherical -Al2Cu precipitates in an Al rich matrix at two different temperatures, for which growth or dissolution occurs. A comparison of the model is made, with the results obtained using the numerical solver DICTRA. The very good agreement obtained for cases where the interfacial mobility is very high indicates that the time discretization procedure is accurate.

Establishment and Solution of the RNC Flow Network Model

2014 ◽  
Vol 548-549 ◽  
pp. 1783-1789
Author(s):  
Li Ying Sun ◽  
Lu Jie Zhen ◽  
Yi Tong Li
Keyword(s):  
Network Model ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Two Phase ◽  
Conservation Equations ◽  
Flow Network ◽  
Cycle System ◽  
Variable Step ◽  
The Mathematical Model

The mathematical model based on graph theory and the refrigerant natural cycle system of gas-liquid two-phase flow network is established. Incidence matrix was used to describe the relationships between the various components. The node conservation equations, branch equations, momentum conservation equation in return circuit and mass conservation equations of system are established. The model was solved by using variable step gird iterative method. Then refrigerant state of each node and refrigerant flow of each branch in network model are obtained. Establishment and solution of the RNC network model provides an effective way for the further performance analysis of system.

scholarly journals Hydrodynamic Escape of Mineral Atmosphere from Hot Rocky Exoplanet. I. Model Description

2020 ◽  
Author(s):  
Yuichi Ito ◽  
Masahiro Ikoma
Keyword(s):  
Molecular Diffusion ◽  
Mass Loss Rate ◽  
Bulk Composition ◽  
Great Influence ◽  
Model Description ◽  
X Ray ◽  
Heating Efficiency ◽  
New Findings ◽  
Low Mass ◽  
Almost All

Abstract Recent exoplanet statistics indicate that photo-evaporation has a great impact on the mass and bulk composition of close-in low-mass planets. While there are many studies addressing photo-evaporation of hydrogen-rich or water-rich atmospheres, no detailed investigation regarding rocky vapor atmospheres (or mineral atmospheres) has been conducted. Here, we develop a new 1-D hydrodynamic model of the UV-irradiated mineral atmosphere composed of Na, Mg, O, Si, their ions and electrons, includin molecular diffusion, thermal conduction, photo-/thermo-chemistry, X–ray and UV heating, and radiative line cooling (i.e., the effects of the optical thickness and non-LTE). The focus of this paper is on describing our methodology but presents some new findings. Our hydrodynamic simulations demonstrate that almost all of the incident X-ray and UV energy from the host-star is converted into and lost by the radiative emission of the coolant gas species such as Na, Mg, Mg+, Si2 +, Na3 + and Si3 +. For an Earth-size planet orbiting 0.02 AU around a young solar-type star, we find that the X-ray and UV heating efficiency is as small as 1 × 10−3, which corresponds to 0.3 M⊕/Gyr of the mass loss rate simply integrated over all the directions. Because of such efficient cooling, the photo-evaporation of the mineral atmosphere on hot rocky exoplanets with massesof 1M⊕ is not massive enough to exert a great influence on the planetary mass and bulk composition. This suggests that close-in high-density exoplanets with sizes larger than the Earth radius survive in the high-UV environments.

Sign in / Sign up

Export Citation Format

Share Document