Question

An anasthesiologist is preparing to anesthetize a patient, who is undergoing surgery to remove her gallbladder. The anasthesia is accomplished with the administration of three drugs, primarily Midazolam (a non-opiod anesthetic), Fentanyl (an opiod analgesic), and gallamine (a long-acting muscle relaxant). Initially, each drug is contained seperate solutions in saline. The concentrations of each solution are 270 ng/mL midazolam, 3 ng/mL of fentanyl, and 42 mg/mL of gallamine. The three solutions are sent through a mixerbefore being delivered to the patient. Help the anasthesiologist plan the dosing rates if the mixed solution needs to be infused at 0.1 mL/min with 0.25 ng/mL of midazolam and 0.02 ng/mL of fentanyl.

A. Write a mass conservation equation for each component

B. Determine the mass flow rate of each drug solution into the mixer

C. Determine the weight fractions of gallamine and saline in the infusion stream

MUST USE MATLAB AND EXPLAIN STEPS. PLEASE>

Answer 1

Data mistake its 42ng/ml rather than 42 mg/ml of gallamine

A. Mass Balance Equation

Let us take V is volumetric flow rate,

x Concentration of midazolam, y concentration of fentanyl, z is concentration of gallamine

Streams 1 is midazolam, 2 is fentanyl, 3 is gallamine

Overall Balance

Balance for midazolam

Balance for fentanyl

Balance for gallamine

given

4 equation and 4 unkonws (V1, V2, V3 and z)

Solving above equation by using matlab code

clc

AX =B

X = linsolve(A,B)

Wx = X(1)*270; \\Weight of midaazolam

Wy = X(2)*3;\\Weight of fentanyl

Wz = X(3)*42;\\Weight of gallmine

rhos = 1; \\density of saline 1 mg/ml

W = 0.1*rhos*(10^6); \\Weight of infusion ng

Ws = W-Wx-Wy-Wz; \\Weight of saline;

Mfz = Wz/W \\Mass fraction of gallamine

Mfs = Ws/W \\Mass fraction of saline

Results we got

Mfz = 0.000042

Mfs = 0.999958

B.

C. Mass fraction gallamine = 0.000042

Mass fraction of saline = 0.999958