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Research Experience for Teachers program

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Minimally invasive surgery is a preferred treatment to the traditional open ... The need for realistic models of soft tissue exploration ... Haptic Interface ... – PowerPoint PPT presentation

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Title: Research Experience for Teachers program


1
Research Experience for Teachers program
My summer with the
  • Andrew Benzing
  • RET Fellow

2
Points of Discussion
  • Introduction to the PRISM Lab
  • Bi-axial Stretcher
  • Creating a Vision by Giving Meaning to
    Data Curriculum Overview
  • Cheerio Lab
  • 5. Taking this back home

3
A need for Research
  • from the PRISM website
  • Minimally invasive surgery is a preferred
    treatment to the traditional open procedures as
    it cuts down on infection rates and recovery
    time.
  • As these relatively new laparoscopic procedures
    are implemented the need for training becomes
    clear.
  • The need for realistic models of soft tissue
    exploration becomes evident. Satisfying this need
    is in fact the work that the PRISM lab conducts
    on a daily basis.

4
Efforts of the PRISM Lab to Satisfy this Need
  • At any given time, several experiments are
    conducted including stretching, grasping,
    probing, and cutting.
  • Once this experimental data is collected a
    mathematical model can be determined that best
    represents the experimental observation of
    force-displacement behavior.

5
Haptic Interface
  • Experimentally observed force-displacement data
    can be used to provide feedback to the surgeon
    through an information enhanced display.
  • In a sense the surgeon will be able to 'feel the
    tissue as in an open procedure.

6
My Role in the PRISM Lab
  • In order to model the stretching of this tissue
    the biaxial tissue stretcher was created that
    stretches tissue in two directions at a constant
    velocity and measures the forces involved.
  • Once we have a measure of the force in relation
    to displacement we can estimate the stress-strain
    relationship of the specimen.

7
Measuring Position
  • We also felt it important to measure position as
    the resistance in stretching and relaxing the
    tissue would vary over the duration of the
    experiment resulting in the arms to move at
    different rates and in turn be at different
    positions.
  • The measuring of the location of the robots was
    achieved through the use of optical encoders
    placed at the end of the motors.

8
Measuring Force
  • The measurement of force both on the x and y
  • axis was taken with load cells that were placed
  • on the stationary arms.

9
Interface
  • All variables involved were monitored using
    an interface where we could set velocity, tare
    force values and program stretch values.

10
RESULTS
  • Initial Trial Testing with Synthetic Materials
  • Rubber (Shown below) - Sorbothan (Latex-Not
    Shown)
  • Hysteresis

11
Preliminary Test Results with Liver
12
Curriculum Plan
  • As taken from the standards outline by the
    National Council of Teachers of Mathematics
  • Recognize and apply mathematics in contexts
    outside of mathematics.  
  • Formulate questions that can be addressed with
    data collect, organize, and display relevant
    data to answer them. 
  • Develop and evaluate inferences and predictions
    that are based on data.

13
Expectations of Students after PRISM visit
  • Given Description of situation provide a graph
  • Provide a reasonable extrapolation of situation
    given graph

14
Labs in Math?
  • SCENARIO Mrs. Al Gebra was sitting down
  • on a Sunday morning getting ready to eat
  • her daily bowl of Cheerios when she spilled
  • some of the dry cereal on the counter. Looks
  • like her lovely husband will have to pick up
  • after her again. As Mr. Al Gebra began to
  • clean up the mess, he considered the area
  • of the counter covered by the cereal. After a
  • deeper investigation, Mr. Al Gebra
  • discovered that a relationship existed
  • between the amount of spilled Cheerios and
  • the area covered by the cereal.

15
Cheerio Lab
  • Procedure Each pair should spill the provided
    Cheerios on their bullseye card. The pairs
    task is to rearrange the Cheerios in an attempt
    to determine which circle radius, in centimeters,
    will contain a majority of the cereal spilt. Once
    the largest radius possible has been covered,
    record the data on the red card as an ordered
    pair, relating the area covered in terms of the
    number of cheerios, x, to the radius of a circle
    in centimeters, y.
  • NOTE A minimum of half of an O must be within
    the area ring to be considered part of the
    coverage area. You are allowed to remove
    individual pieces of cereal to better fit within
    a circle, but may not add cereal.
  • TOUGHIE Derive a formula that relates the
    radius of a circle, R , with the number of
    Cheerios contained in the circle, c, where R is a
    function of c.

16
Follow Up
  • R (c) __________________
  • DISCUSSION QUESTIONS
  • 1.) Evaluate and interpret the real-life meaning
    of the following expressions.
  • a.) R ( 5 ) b.) R ( c ) 5 c.)
    5 R ( c )
  • 2.) Identify the coefficient contained within the
    function that produces a stretch. What do you
    suppose is the real life significance of this
    figure?
  • 3.) General Mills has decided that they would
    like to enlarge the Os in their cereal to 1.25
    centimeters. How will this impact the graph? How
    will this impact the function rule?
  • 4.) Let us redefine the variables of the
    experiment so that the number of cheerios is
    dependent on the radius that is to say the number
    of Cheerios, C, is a function of the radius r.
  • a) Which function that we have studied would
    best resemble C ( r )?
  • b) What is the relationship between C ( r ) and
    R (c ) ?
  • c) What is the equation for C ( r ) ?

17
  • In relating the number of Cheerios within the
    circle truthfully
  • we are considering area. So students should
    consider the
  • relationship between area and radius.
  • We will recognize the notation Ao and ro to
    represent the
  • area and radius of the bullseye.
  • The given area formula provides us with a formula
    where c
  • is a function of R however we need a formula
    where R is a
  • function of c. Therefore we must consider the
    inverse.
  • Now we have R which is a function of A, but not
    of the
  • number of Cheerios.

18
  • In considering the Area of the bullseye in
    terms of
  • the number of cheerios we can say
  • and we also know the area of 1 Cheerio
  • where Ac and rc represents the area and radius of
    1
  • cheerio
  • therefore we know

19
How to take home?
  • NSF Grant for Instructional Materials
    Development Program
  • Math and Science Department meeting
  • Delaware County In-service for Math and Science
    Teachers on November 4th Technology In Action

20
A special thank you for special people
  • The group of graduate students below each have
    assisted me on
  • numerous occasions and have been extremely
    patient in dealing
  • with my never-ending questions. Dedicated and
    hardworking, the
  • group below is the heart of the PRISM lab.

21
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22
I almost forgot one more thank you
Dr. Desai
23
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