Lab Write-up for Lab #7 CATHETER MODELING
BioE431

Abstract
Catheters have many uses when it pertains to medicine, a simple design that consists of a long narrow tube connecting to the body externally or internally and the other end to an apparatus or module. It is a negative system meaning the catheter is always connected at both ends making it a closed system. This setup can be / is being used for medicine delivery, fluids input and output, measuring volume displacement and many other operations. We are constructing a similar catheter module to measure and display a step response to a catheter loosing its negative/closed environment. To achieve this data we have a tube filled with water connected to a pressure sensor that doubles up as a transducer converting the pressure change as an electrical signal, which via software is being graphed. The other end of the catheter is connected to a funnel with a balloon atop and this funnel is junctioned using a 3-way stopcock. The tube is filled with water end to end, the balloon attached on the funnel is blown up which in turn puts pressure on the water which puts pressure on the pressure sensor, that transudes the pressure difference in to an electrical signal and LabView software displays that signal as a graph. Documenting and analyzing the step input when the balloon is popped is the purpose of this lab.
Introduction

The purpose of this lab is to build a catheter system, with an inflated balloon applying pressure to the catheter being recorded by the computer and being graphed. While we analyze the data when the balloon is popped and a step input is recorded.

Procedure
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Constructing the set up above with the catheter filled completely with water. We used a blood pressure cuff pump to fill the balloon with air while keeping the water in the tube locked off via the 3-way stopcock. Having the setup completed we initialize data recording and observe the graph, at this point the balloon is popped and the step input is recorded.

Results:

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2.
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Graph 3: Impulse Response [pic]
Graph 4: Frequency Response

5. Estimates from Normalized Step Response
T = 3.7 – 1.5 = 2.2 s y1= 1.07 y2= 1.04

Λ = ln(y1/y2)
Λ = 0.0284 ________
Z = Λ / √ 4π2 + Λ2
Z = 0.00452 ______ fn = 1 / (T * √ 1 – Z2) fn = 0.45455
Frequency response for 0.1 – 110 Hz
High pass filter C1=47microF therefore; cutoff F=0.02Hz
Low pass filter C2=0.01microF therefore; cutoff F=106Hz

6. s(t) = 1 – ( e-.0129t( .00452sin(2.856t) + cos(2.856t) ) )

Comparison of Model and Actual Step Response

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7. Frequency Response

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8. The frequency and magnitude increase in proportion to each other. But because our experiment was not a complete success we are unable to derive the value for Z and Fn.

Discussion: The purpose of this lab was to observe and analyze the step input created when pressure is dissipated abruptly. Having fluid filled catheter creating a pulse response via a pressure sensor connected to a waveform graph and data recorder, we will use both the time domain step response and the frequency response to characterize the system, validating Relationship between the step response and impulse response of a system. This extra vascular catheter can be described using a second order system, 2nd order system parameters are defined .

We obtained the frequency response, impulse response, the signal noise but all the numbers seem off target probably because of bad data collection on our part. Having all the equations we were able to understand the potential of this extra vascular catheter and its uses.