BME 307 Exam 3 Review

Flux

100

Define flux

amount of material crossing a unit area normal to the direction of transport in a given unit of time

200

What is the dilute-solution assumption? (criteria)

solvent concentration is much greater than Ci

300

To derive Fick's First Law, what conservation equation do we start with (ie what is conserved?)

mass

400

When considering a diffusion limited protein adsorbing to the surface, what is the flux of the protein at the surface z=0?

sqrt(Dij/(pi t)) Co

500

In setting up the mass balance for cylindrical coordinates, what expression represents flux in - flux out?

(N_ir|_r(r) - N_ir|_{(r + delta r)}(r+delta r))* 2 pi L

Diffusion

100

At what distances does diffusion become inefficient?

100-200 microns

200

What does the steady state assumption in a diffusion problem tell you?

dCi/dt = 0

300

What do we typically use Fick's 2nd Law to calculate?

dC/dx

400

When looking at radial diffusion, what is the surface area of the inner shell?

4 pi r^2

500

When calculating the equivalent radius, what is the equation and define each parameter.

(3V/(4 pi N_A))^1/3

N_A is avogadro's number

V is partial molar volume of the protein of interest

Protein Transport

100

To calculate a protein's transport in interstitial space when there are no significant effects from diffusion, what assumption should we make about the shape of the protein?

spherical

200

What equation can you use to calculate the estimated displacement after 1 minute? Assume transport occurs in 3D.

<r²> = 6 D_ijt

300

Continuing with the calculation of the protein's transport, what equation do you need to calculate D_ij?

D_ij = k_bT / (6 pi mu R)

400

Assume that the solvent viscosity is .69 cP and the molar volume is 23,500 cm³mol^-1.  What is R?

2.104 x 10^{-7 cm}

500

What is the estimated displacement? (Remember that we're assuming 37 degrees C, .69 cP viscosity for the solvent, and 23,500 cm³mol^-1 after one minute.

.0237 cm

Estimating Diffusion Coefficients

100

We're considering a protein that has been measured to be 3.5 nm x 2 nm x 2 nm.  What equation would you use to estimate the mean frictional drag coefficient using Stokes-Einstein with the shape of a prolate ellipsoid?

look at equation sheet

200

What does mu represent in this equation

solvent viscosity

300

We're considering a protein that has been measured to be 3.5 nm x 2 nm x 2 nm. What is the mean frictional draft coefficient?

2.34 x 10^-8 g/s

400

We're considering a protein that has been measured to be 3.5 nm x 2 nm x 2 nm. What is the estimate for the diffusion coefficient?

1.73 x 10^-6 cm²/s

500

We're considering a protein that has been measured to be 3.5 nm x 2 nm x 2 nm. It's diffusion coefficient in 20 degree C water was measured at 1.07 x 10^-6 cm²s^-1. What is your percent error?

61.76%

Drug Eluting Stent

100

Imagine we have a drug-eluting stent. The drug is allowed to diffuse into the tissue and the total amount of the drug entering the tissues is measured. Drug concentration in the lumen is assumed constant. Ignore curvature of the blood vessels and assume semi-infinite diffusion.

Determine an equation for the uptake, M, over an area A by integrating the product of flux times CA from time 0 to t'.

M=integral from 0 to t N_ix(x=0) A dt

200

Imagine we have a drug-eluting stent. The drug is allowed to diffuse into the tissue and the total amount of the drug entering the tissues is measured. Drug concentration in the lumen is assumed constant. Ignore curvature of the blood vessels and assume semi-infinite diffusion.

Determine an expression for the diffusion coefficient as a function of time.

D_ij = pi / 4t (M/CoA)²

300

A drug eluting stent infuses long enough that the concentration of the drug in the blood is constant at Cb. Assume the drug concentrating in the outer part of the artery is Co.  If the inner part of the artery is Rb and the outer radius is Rb, what is the concentration at Rb?

Ci = phi Cb

400

A drug eluting stent infuses long enough that the concentration of the drug in the blood is constant at Cb. Assume the drug concentrating in the outer part of the artery is Co.  If the inner part of the artery is Rb and the outer radius is Rb, what is the concentration at Ro?

Ci = phi Co

500

A drug eluting stent infuses long enough that the concentration of the drug in the blood is constant at Cb. Assume the drug concentrating in the outer part of the artery is Co.  How would you find the flux of the drug into the artery at Rb. (neglecting chemical reactions)

At steady state the derivative with respect to time is zero. So 1/r d/dr (r dCi/dr) = 0.

integrate twice to get Ci = A ln r + B

use boundary conditions to solve for A and B

Get concentration and plug it into equation for flux