Project Help Notebook by Keith Stroyan

Help NoteBook Copyright 1998 by Academic Press, Inc. - All rights reserved.
Modify this Notebook to prepare your project report.

Project 16: Kidney Function by Drug Concentration

by A. Student and B. Pupil

with technical help from Da LabMonitor and Help Notebook

Initialization

Needs["Graphics`Colors`"];

My Project Introduction

Write this last.  Begin with the basic question and state your main finding clearly, but with few technical details.  You might even modify the title of this section to make it more interesting.

Beginning Explorations or Computer Experiments

Warfarin Data for Project 16:

The following  are similar to data on the anti-coagulant warfarin.  They are given in pairs , {t,c} = {time (hrs), concentration (mg/l)}:

data = {{.5,64.},{1,36.},{1.5,23.},{2,18.},
{3,14.},{4,14.},{6,12.},{8,12.},{10,11.},
{12,10.},{24, 8.},{36,6.},{48,4.0},{60,3.0}};
dataPlot = ListPlot[data,AxesLabel->{"t","c"},PlotStyle->Blue,Prolog->AbsolutePointSize[4]];
TableForm[data]

{times, concens} = Transpose[data]
times
concens

The Semilog Plot of Blood Concentrations

logCons = Log[concens]

logData = Transpose[{times,logCons}]

logPlot = ListPlot[logData,AxesLabel->{"t","Log[c]"},PlotStyle->Red,Prolog->AbsolutePointSize[4]];

Finding the Exponential Parameters

The Log-Linear Tail (Exploration 16.5 in the written project.)

Following is technical help with fitting lines to data.  Do you really think that using only the last 4 points is a good idea?

tail = Take[logData, -4]

f = Fit[tail,{1,t},t];
tailPlot = Plot[f,{t,0,60},AxesLabel->{"t","Log[c]"},
Ticks->{{20,40,60},{1,2,3,4}},PlotStyle->Brown,DisplayFunction->Identity];
Show[tailPlot,logPlot,Prolog->AbsolutePointSize[4],DisplayFunction->$DisplayFunction];
f

Removing the Tail to find the Head (Exploration 16.6, 16.7, 16.10)

Read Exploration 16.6, 16.7, 16.10 and solve them with the help of the following.

h2 = 0.026
b2 = Exp[2.7]
remainders = concens - b2 Exp[ - h2 times]

headData = Transpose[{times,Log[remainders]}]

headPlot = ListPlot[Take[headData,6],
	AxesOrigin->{0,0},AxesLabel->{"t","Log[c]"},
	Ticks->{{1,2,3,4},{0,1,2,3,4}},Prolog->AbsolutePointSize[4],PlotStyle->DarkGreen];

g = Fit[Take[headData,4],{1,t},t];
headLine = Plot[g,{t,0,4},AxesLabel->{"t","Log[c]"},PlotStyle->Green,DisplayFunction->Identity];
Show[headLine,headPlot,Prolog->AbsolutePointSize[4],DisplayFunction->$DisplayFunction];
g

b1 = Exp[4.8];
h1 = 1.7;
cA[t_] := b1 Exp[-h1 t] + b2 Exp[-h2 t];
curvePlot = Plot[cA[t],{t,0,60},AxesLabel->{"t","c"},PlotStyle->Purple,DisplayFunction->Identity];
Show[curvePlot,dataPlot,Prolog->AbsolutePointSize[4],DisplayFunction->$DisplayFunction];
cA[t]

The Physical Parameters

Solve Hints 16.12, 16.13 and explain with the following help.

cI = cA[0]

vB = 100/cA[0]

w1 = b1/cI
w2 = b2/cI

h1 - w1 (h1 - h2)

k2 = w2 (h1 - h2) + h2

k3 = h2 h1/k2

k1 = h1 + h2 - k2 - k3

vT = k1 vB/k2