Calculating Elastance using an Electrical Model of the Left Hea by mikesanye


									    Investigating A Elastance Catheter In A Micro-Gravity Environment

               Biomedical and Cardiovascular Engineering

                     The Little E Crew

                      Academic Institution
                 North Dakota State University
        Department of Electrical and Computer Engineering
                          PO Box 5285
                      Fargo, ND 58105-5285

                   Student Investigators
Nathan Grenz, Biomedical Engineering Senior – Flyer
Greg Rise, Electrical Engineering Senior – Flyer
Corey Schwartz, Electrical Engineering Senior - Flyer
Travis Schmidt, Electrical Engineering Senior - Flyer

                          Scholar Team
Mike Newell, Electrical Engineering Junior- Alternate Flyer
Jordan Lucht, Electrical Engineering Sophomore -Alternate Flyer
Chris Yost, Electrical Engineering Freshman -Ground Crew
Patrick Nolan, Electrical Engineer- Freshman-Ground Crew

             Patrick Nolan, Freelance Journalist - Flyer

                        Contact Person
                         Corey Schwartz
                          (763) 360-0166

                       Supervising Faculty
                        Dr. Dan Ewert
                          (701) 231-8049
2 Flight Week Preference ....................................................................................................... 3
3 ABSTRACT ............................................................................................................................. 3
4 Test Objectives........................................................................................................................ 3
5 Test Description ...................................................................................................................... 4
6    Justification for Follow-up flight................................................................................. 11
7 Experimental Safety Evaluation ................................................................................... 12
  Use of water in a compliant material: ............................................................................. 12
  Rotating machinery: ............................................................................................................ 12
  Electrical Hazards: ............................................................................................................... 12
  Sharp corners and protrusions: ....................................................................................... 12
8    Outreach plan................................................................................................................... 13

2 Flight Week Preference

1. Flight Group 2                         March 17 to March 26, 2005
2. Flight Group 1                         March 3 to March 12, 2005
3. Flight Group 3                         March 31 to April 0, 2005


       In a microgravity environment the mechanical properties of the heart may
undergo changes; in a zero gravity environment the heart becomes more spherical, and
at higher gravities the heart elongates. These conformational changes may contribute
to the changes in the mechanical properties of the heart. The objective of this project is
to measure the elastance in a compliant heart model with a prototype medical catheter
to determine if gravity affects the elastance.

        A water-filled heart model will be monitored with pressure sensors during the
operation of the catheter. The prototype catheter will be inserted into the heart model,
and creates small volume perturbations at relatively high frequencies – from 20 to 60
Hz. This known volume change will create a corresponding pressure change, which the
pressure transducers will measure. The volume-pressure relationship can then be used
to determine the elastance measured in the heart model. The data collected from the
differing gravities will be analyzed with previously collected data at 1-G to determine the
change in elastance.

        Long term space flights and differing gravitational fields of other planetary
systems (mars) may create remodeling affects in the cardiovascular system. Knowing
the mechanical property changes in microgravity environments can help prepare, train,
or develop systems to compensate for them during long durations in reduced gravity. In
addition, this study would help to characterize the prototype catheter, and determine
how the catheter behaves in different orientations and gravities. The change in the
mechanical properties of the heart also occurs in patients with failing hearts and
knowing these properties may help match ventricular assist devices with the heart. The
ability to understand the changing elastance in different environment will help create
possible diagnostic and treatment techniques for different environment or disease

4 Test Objectives

It is known that exposure to microgravity causes many changes in the body, including a
fluid shift to the upper body and this can cause remodeling of the cardiac cells.
Remodeling is known to alter cardiac muscular visco-elastic properties, which can
adversely affect cardiac performance [3]. The objective of this study is to determine the
effect of gravity upon the visco-elastic properties of a heart model using a new prototype
medical catheter based on volume changes within a heart model.

We conjecture that changes in gravity will cause conformational volume changes in our
heart model and that conformational changes will cause altered visco-elasticity. The

model should become more spherical and relaxed in microgravity and be elongated and
stressed in the presence of higher gravity. (Elasticity can be a function of the geometry
of the object). We hypothesize that these geometrical changes during varying
gravity conditions will affect the visco-elastic properties of our model. It is hoped
that this work provides some insight into how the heart may change in altered
gravitational environments. It is believed that a catheter of this type will someday be
used to track the alterations in the cardiac function of patients who experience extended
bed rest in hospitals or undergo therapy for heart failure on earth, leading to better
diagnostic techniques and more potent therapies. This is a follow-up experiment
from a previous flight which used a different technique of generating the volume
change based on prior research.

Specific Aims:
      Test a prototype medical catheter in a compliant heart model.
      Measure pressure and volume signals during zero-G and pull-out           gravitational
      Measure pressure and volume signals during lunar and Mars                gravitational
      Calculate the visco-elastic properties of the heart model for all four   gravitational
      Statistically compare the visco-elastic properties for all four          gravitational

5 Test Description

During the experiment, a prototype medical catheter will produce small, rapid volume
changes inside a heart model (a balloon-like chamber filled with water) using a
mechanical apparatus. By measuring the pressure inside the model chamber and the
volume change induced by the catheter, visco-elastic properties can be calculated using
a newly published cardiac mathematical model [1,2]. We currently testing the system to
collect this data on the ground and establish normal values of visco-elasticity at various
heart model volumes.

The experiment will be performed on a rack to stabilize the test model, instrumentation,
and data collecting equipment. The heart model will be instrumented with 2 or 3
pressure transducers, the catheter, and contain an initial volume of de-aerated water.
Catheter induced volume change will be accomplished by running a cable through a
hollow casing and attaching a hinged “cage” with a deformable shell surrounding it. An
electric motor coupled to a rotary-to-linear motion piston will operate the cable. As the
cable is pushed and pulled, the cage will mechanically expand and contract to produce
a change in volume inside the model, which creates the pressure response. We plan to
create a volume change of about 2-4 ml from 20 to 80 Hz.

The test process starts with filling the heart model to an initial volume. This places the
test results at a know point in the elastance curve, and allows for determination of the
visco-elastic properties during data analysis. Once the volume has been inserted, the

motor-piston unit is started to create the volume perturbations. The volume change
frequencies will be varied from a slow rate to a faster rate as the operators monitor the
output of the pressure and volume waveforms. Portions of the frequency range from 20
to 80 Hz may contain the resonance frequencies of the system and may not collect data
with significance. Frequencies on either side of the resonant frequency will provide
useful information.

Once the motor and piston have been set to a desirable frequency range, the test will
run without operator action, other than to watch the output for signs of trouble, and to
monitor the integrity of the mechanical assembly. After several parabolas of collected
data, a new frequency will be set and more data will be recorded. The test process will
continue until the flight has concluded. An accelerometer will be used to measure the
acceleration due to gravity for each portion of the flight so data can be separated into
the appropriate category for data analysis.

So far the data collected from the methods described have been accomplished using
latex balloons as the heart model. Several frequency ranges have proven successful,
but the elastance of these balloons may have other effects in the different gravity fields.
A search is in progress for a heart model which provides a higher elastance and a small
resonance frequency range.

Once we have collected data from several steady state runs at one volume, a computer-
controlled pump will change the volume every 5 parabolas so we can repeat the same
experiment at other volumes in the heart model. This change in volume will shift the
measured visco-elastic properties of the chamber, and allow for a determination of the
sensitivity of the catheter. A laptop computer with a program written in Labview
captures the pressure transducer signals and the piston position signal. The pressure
transducer voltages directly relate to the measured pressure, and the piston position,
measured with a linear displacement voltage transducer, records the volume
perturbation. The pressure and volume change signals display in real time, to allow the
operator to see if any problems occur in the test setup. After each flight, the laptop will
be taken for data analysis and determination of the visco-elasticity of the heart model.
Using a model created in Matlab, the pressure-flow relationship will be constructed and
from this, the visco-elastic properties can be determined.

A mechanical analogy for the visco-elastic properties can be created using two springs
in parallel and a dashpot. The dashpot acts as the frictional component, similarly to a
shock absorber on a car. The springs store energy during one phase of the heartbeat
and release it during other phases of the heartbeat. One spring, e(t) can be modeled as
a variable spring, and is the driving force of the heart. This is the contractile element of
the heart muscle. The heart contraction can be represented by spring constant of the
spring increasing e(t). This raises the force supplied by the spring, and thus drives the
piston up – creating the fluid flow out of the chamber.

The second spring, e1, represents the 'sponginess' of the heart. In order for a
contraction to drive blood out of the heart, this spring force must first be overcome. So,
during the initial stages of the contraction, before the heart can generate enough force

to forcibly eject the blood, it must first compress (or in the model below, elongate) these
spongy elements in e1. Once e1 has been fully compressed, then the flow of fluid will
proceed, dampened by R, and out into the arterial system. Conversely, when the
contraction of the heart ends, the compression of e1 actually helps the heart to refill. In
the heart, once the contraction ends, the heart undergoes a period where the muscle
expands on its own – presumably due to the springy effectors that were compressed
elongating again – and during diastole, a period exists where the ventricle actually
draws in blood on its own, called 'diastolic suction'.

By careful analysis of mathematical models and simulations, three regions of interest
were discovered which apply to this experiment. During diastole, when the ventricle fills
before ejecting, e(t) is assumed to be small, and with no ejecting volume R is negligible,
and thus the major pressure generating element from a volume perturbation would be
e1. This can be measured again after the heart finishes the contraction and starts to fill.
Thus there are two portions of a heartbeat where e1 can be independently measured
using volume perturbations.

The third portion of interest during the heartbeat is at the peak of an isovolumic
contraction. During this portion of the heartbeat, the contractile force created is the
largest. This produces the largest driving force for flow, and the resistance plays the
largest role. From this peak, the value of R can be calculated, as well as the total

capacitance. Once R and e1 are known, the assumption can be made that these are
constants during a heartbeat. How true this assumption is remains to be seen, but
Ewert,, used this assumption and were able to generate results. From R and e1 in
the waveforms, finding e(t) reduces to a simple substitution problem.

This is the mathematical model which will be used in Matlab to generate the visco-
elastic properties of the heart model. Since the model remains at a constant volume
during the volume perturbations, a direct contractile model cannot be created.
However, the constant volume heart model acts like the heart in diastole to a large
extent. This allows for calculation of e1 directly, and given a large enough number of

data points, a method for R can be teased out. The calculation for e1 starts by finding
the flow and the pressures in appropriate units. Flow is just the derivative of the volume
signal, which can be easily done with any discrete derivative method – such as in
Simulink, a graphical mathematical manipulation program within Matlab.

The conversion from the measured voltages of the pressure transducers to the true
pressure of the model can be achieved through a direct linear equation. The pressure
transducers currently in use have a stated offset of 0 Volts, and have a sensitivity of 400
millivolts per 1000 pascals. Using the conversion factors, the equation becomes

          1 kpa   760mm Hg
voltage                         mmHg
          400mV   103.5kpa

This leaves us with the discrete time domain data in units of mm Hg.

Similarly, the conversion of the volume signal can be done with the collected linear
voltage transducer data. The rotary displacement of the piston follows a sinusoidal
curve. At this time, a detailed analysis of the actual mechanical volume displacement
hasn't been done to enough accuracy to satisfy the question of whether the true volume
displacement is sinusoidal, but the differences may be so small that little error is
introduced with this assumption. Converting the piston displacement to the volume
displacement requires only two operations in any mathematical package – shift the
voltage minimum to the x-axis, and multiply the data by a scaling factor so the maximum
value is the peak volume displacement.

For example, if the piston voltage signal has the equation 5*sin(2*pi*f*t)+3, but the
maximum volume displacement is actually only 2 mL, a conversion of 1/5*(voltage – 2)
would produce a sinusoidal output of 1*sin(2*pi*f*t)+1. This retains the true frequency
components, but shifts the signal down so it oscillates from 0 to 2 mL, the true volume
displacement from the catheter. The catheter volume will not vary during the test, since
it is determined by the mechanical construction of the device, and that will not be altered
during the flights, or between flight days.

After converting the raw pressure and volume signals to the true pressure and volume
signals, data analysis can begin. Since the visco-elastic properties of the heart and
heart model translate into the electrical model equivalent, these properties can be
simply called the impedance of the system. The impedance of an electrical model can
be represented by either the time domain analysis or the frequency domain. The
current mathematical model actually uses the frequency domain, to scale well with
frequency without adding a large amounts of calculations.

To translate the time domain signals from the experiment to the frequency domain, a
reference point must be established. The mathematical model uses the zero crossings
on the volume change. This reference point doesn't drift, and the constancy in the
amplitude of the volume change makes this a very stable point to look for. The
pressure signal is then referenced to the volume signal to make everything as
consistent as possible. An example of the volume signal is shown below.

Essentially every cycle of the volume perturbation will be extracted and examined in
isolation. The dFFT – discrete fast Fourier transform - will be done on every cycle of
the volume perturbations. Isolating each cycle will make the dominant frequency of that
cycle the first harmonic, which makes mathematical analysis quite easy, and if the
experiment doesn't pick up noise, or have other unforeseen problems, the higher
harmonics should actually be statistically insignificant, and can be ignored.

This allows for calculating the impedance of the system – and visco-elastic properties –
by dividing the dFFT of pressure by the dFFT of the flow. This will produce the real and
imaginary components of the impedance of the heart model. The real components of
the dFFT’s will calculate the magnitudes, and the imaginary components represent the
phase. Dividing the magnitudes produces the resultant length of the impedance vector,
and subtracting the phases produces the direction of this vector. A sample vector is
shown below.

 Since the heart model will not contract or experience any c(t) effects, the two elements
of the impedance will be the resistance (the real component) and the elastance (the
imaginary component). Using these two components, the real component directly
corresponds to the resistive element, while the imaginary component corresponds to the
elastance. Once the vectors are known for each cycle of the data, the resistive and
elastic values can be extracted and then compared for use.

From this, the static and dynamic elastance of the heart model can be compared. A
direct comparison will be conducted to determine whether the catheter can actually
determine the visco-elastic properties with dynamic methods in normal gravity
conditions, and how accurately. In essence, this is the comparison between the static
and dynamic methods.

After careful examination of the static and dynamic testing, the results of the dynamic
tests will be compared between differing gravity fields. The visco-elastic properties from
1G will be compared with 0G and ~2G to quantify any differences. The hypothesis
remains that due to the conformational changes induced by the differing gravity fields,
the visco-elastic properties will be different. A statistical analysis, such as a difference
test, or an anova, will be done to determine significance.

If equipment and room allow, another similar system can be rigged up to allow for a
pseudo-static test for visco-elastic properties. This could be done by connecting a very
accurate screw-drive pump to a similar heart model and inject and withdraw a set
volume at a relatively slow rate – up to 60 mL/min. The changes in the properties can
then be compared both statically and dynamically. Due to the use of different systems,
there could not be any direct comparison between the static and dynamic
measurements, but together the changes should vary by similar amounts.

From this, we expect to learn several things. Most importantly is whether the visco-
elastic properties of a compliant system are altered in different gravitational fields. The
flight will provide the opportunity to explore an aspect of physiology that is difficult to
achieve and account for with testing in a ground based lab. The geometric
conformational changes as a result of the different gravity fields cannot be achieved for
most lab conditions except for a reduced gravity flight. Conformational changes when
extrapolated toward long term heart remodeling conditions may help shed some light on
the process by which heart disease starts or progresses into the deleterious effects
which impact patients.

The team also expects to learn how the elastance catheter works by backing up the
research in the lab with research in a non-laboratory setting, which may help guide the
development of future iterations toward a clinical setting. One other item of interest is to
show students of different scholarly levels how the research process works, rather than
just by observations in a lab setting.

This project also will incorporate students from both North Dakota State University in
Fargo and the University of North Dakota in Grand Forks, in a combined school project.
This is the result of meetings with the North Dakota Space Grant Consortium which
helped to guide the teams and encouraged us to participate by allotting money for the
cooperative research and travel. This may lead to both engineering schools combining
in other ways, since the UND medical school can be tightly integrated with future
biomedical and space research.

6         Justification for Follow-up flight

    Last year we attempted to calculate the change of elastance due to gravity in a heart
    model. Upon analysis, we discovered several problems with the methodology. The
    method chosen for volume changes produced a limited test time (one third of the
    total flight time) due to material failure, the material's behavior interfered with the
    statistical distinction between elastances at the various g-levels, and the imparted
    volume could not be deemed constant. Based in part on what we learned from this
    experiment, we have developed the new elastance catheter, that we feel will
    overcome these limitations.

    The previous method used a piston and diaphragm system to change volume. The
    compliance of the diaphragm added an unknown variable and made absolute
    volume changes difficult to determine. Additionally, the natural vibration modes of
    the diaphragm created a 'ringing' effect, adding high frequency waveforms. The
    higher frequency calculations are vital for future medical implementation. The
    system also failed sooner due to erosion of the diaphragm by the piston.

    The prototype catheter uses a completely enclosed mechanical system inserted into
    the heart model. This improves the process since there are no unknown variables
    created by the induced volume change, reducing the volume error. This method
    requires no contact between surfaces, so material failure is not expected. The

    prototype aslo creates the volume change internal to the model, so 'ringing' due to
    surface oscillations is not expected to be significant at the frequencies of interest.

    This will produce stable waveforms, allowing for identification and filtering of
    electrical noise. These changes will produce more accurate calculations. The
    prototype catheter also has better frequency characteristics at crucial high
    frequencies. Along with better pressure sensors and more advanced
    instrumentation, the new data collected is expected to definitively determine the
    effect gravity plays on elasticity.

7      Experimental Safety Evaluation

The experiment contains only a few overall safety concerns that we are aware of. As
this is a follow-up flight, and the first flight went very safely, we believe the experiment to
be designed with safety in mind. Specifically the items of concern are:

Use of water in a compliant material:
 The system will be pressurized to a small amount – between 1 and 10 mm Hg above
atmosphere. If the system were to leak or break, water would be floating around in zero
gravity, or forcibly spilled on the equipment rack. To prevent this, the water container
will be enclosed in a case with sponges on the top and the bottom. This will help to
absorb the water and prevent free-floating water damage.

Rotating machinery:
  The motor and piston will be running at between 1500 and 4000 rpm. This presents
the possible hazard of getting entangled in equipment and also projectiles if the
equipment flies apart. The solution to this is to build a plexiglass enclosure to prevent
outside material and personnel from contacting the machinery, and to contain any flying
objects should the mechanical structure come apart. The motor and piston will be
securely mounted to the base of the rack.

Electrical Hazards:
 The equipment used will be running on 120 VAC. This leads to possible electrical
hazards. To prevent this, there will be electrical fuses to stop the motor on an
overcurrent condition, or fault. There will also be a kill switch to power down the entire
system, accessible from the top, without too much difficulty, should anything drastic
happen. The laptop will contain a battery, to prevent data loss in the event of a
complete system shutdown.

Sharp corners and protrusions:
 Since the rack will be either the welded aluminum structure that has flown on three
previous flights, or a new construction with brackets and bolts, there will be sharp
corners. To minimize this hazard to personnel, all the sides and top and corners of the
rack will be encased in a foam material to soften any impacts.

8      Outreach plan

We feel that the privilege of experiencing a micro-gravity environment gives us the
further opportunity and responsibility to motivate young people to keenly pursue math
and science education, as well as to supply the results of our experiment to those who
have interest in the unique data acquired. We will hold a press conference to create
excitement throughout the community about things happening at North Dakota State

Education motivation

After performing our proposed experiment, we plan to take our experience to high
schools, junior highs schools and elementary schools. We believe that students (K-12)
will benefit and be excited to see the variety of opportunities that math and science
applications can be applied to. Specifically we intend to target underrepresented
groups in engineering – women and minorities.

We believe that sharing our experiences in the K-12 setting, will allow young people to
see the exciting opportunities that they could have as university students (and future
engineers and scientists). Statically, girls of ages 11-14 are “at risk” for losing interest in
math and science. Thus our presentation will be tailored to this group to help show
them that they are on equal grounds as boys of their same age.

The presentation will be composed of a brief power-point description of our project,
along with video illustrating the parabolic flight experiment and ability to see our actual
design and a brief demo. Finally, some of the future medical uses of the device will be
discussed and their benefits.

Listed below is a list of schools in our region:
 Madison Elementary
 Washington Elementary
 Park Christian School
 South Fargo High School
 Moorhead Junior High
 West Fargo Junior High
 North Fargo High School

We will also relate our experiences at the North Dakota Science Olympiad on April 16,
2005. The North Dakota Science Olympiad is a statewide science fair for students in
grades 6-12. We feel that this would be an excellent opportunity to expose young
students to the opportunities and benefits of an education in science and technology.
We will also be holding demonstrations during engineering week at North Dakota State
to show prospective students all the fun and exciting opportunities that will be available
to them at North Dakota State.

In order to relate our experiences to our fellow students and the faculty at North Dakota
State University, we will be giving a presentation on our micro-gravity experiment in

April of 2005. As part of this presentation, we will describe why a micro-gravity
experiment was necessary, the means by which we performed the experiment, and the
results of the experiment. Since this audience will consist primarily of electrical
engineers, the focus of the presentation will be on the technical aspects of how we
designed, built, and operated our equipment, as well as how we achieved our goals as
a team. Also we will describe the future advancements of our device and its medical

Having the opportunity to represent North Dakota State University school of
Engineering, we feel that it can also produce several benefits for the local schools, and
especially to the schools that may not have the facilities to engage in serious science
programs. Reaching out to these schools can provide the encouragement and support a
student may be lacking in order to choose a career in science. A future NASA engineer
may be making a choice now whether to continue in science or to change to some other
field. Having the opportunity to present the project, as a student to a student, may
cement the decision, and create the enthusiasm and energy to pursue a career in

At all presentations, we will inform the listeners of our web site, which will have an
online copy of our final report as well as other interesting, fun, and motivational material.
A pre-flight site is available at the URL *****

Experiment results distribution

Research done by Dr. Ewert of NDSU, Dr. Koenig of University of Louisville, Dr. Shaq of
Meritcare Hospital, and Dr. Simon McGuirk of England, will have a direct correlation to
our experiment. They will be interested in knowing the results of our proposed
experiment. We anticipate that this project will produce valuable data on how well the
instrumentation measures the elasticity in a micro-gravity environment. This will
hopefully lead to future research in this area of cardiovascular technology. After the
flights are completed and the data is analyzed, we will attempt to publish a report in a
biomedical journal as a means of providing feedback to the biomedical community.


  1. Koenig, SC, Convertino VA, Fanton JW, Reister CA, Gaffney FA, Ludwig
     DA, Krotov VP, Trambovetsky EV, and Latham RD. Evidence for increased
     cardiac compliance during exposure to simulated microgravity. Am J Physiol
     Regulatory Integrative Comp Physiol 275: R1343-R1352, 1998

  2. Templeton, G, Adcock R, Willerson JT, Nardizzi L, Wildenthal K, and
     Mitchell JH. Relationships between resting tension and mechanical properties of
     papillary muscle. Am J Physiol 231: 1679-1685, 1976

  3. Ewert, D, Wheeler, B, Doetkott, C, Ionan, C, Pantalos, G, Koenig S,. Effect of
     Heart Rate, Preload, and Afterload, on the Viscoelastic Properties of the Swine
     Myocardium, Annals of Biomedical Engineering 32: 1211-1222, 2004


We have obtained funding from the North Dakota Space Grant for $9000, $6000 for NDSU and
$3000 for UND. We also anticipate receiving $2000-3000 from North Dakota State University
from sources including the President and Vice President and the Department of Electrical
Engineering. The estimated budget is presented in the table below.
Description                                  Estimated Cost
Travel (food, mileage, etc.)                 $2500
Equipment                                    $1500
Hotel                                        $6000
Experiment Rack                              $1000
Total                                        $10000


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