BENG 112A Homework Assignment 6: Design a Device to Test an Artery Subjected to Inflation, Stretch and Torsion

Due: Tuesday March 6th at the beginning of class

The goal of this assignment is to design a test device that measures the mechanical responses of an artery subjected to simultaneous inflation, stretch and torsion. Main components of the design project will include:
-Identifying a specific type of artery and species that will be tested and explaining the importance of your choice.
-Illustrating how the vessel will be loaded, coupled to transducers and how strains will be determined
-Performing a stress analysis of a typical artery in Continuity using a published constitutive law and material parameters, and using the results to specify suitable specifications of your transducers such as sensitivity, accuracy, and full-scale deflection.

  1. First, identify a specific type of artery from a specific species such as human aorta or mouse coronary artery. Explain your choice of vessel type. What makes this vessel important? i.e. Why would you want to test it? Explain your choice of species. Why is this species a useful choice? What are it's advantages and disadvantages? It would be a good idea to choose a vessel and species for which a constitutive law and parameters have already been published, but if you don't you can explain why you think the constitutive law that you choose is a useful approximation for your vessel type and choice.
  2. Provide a detailed sketch or sketches of the test apparatus with adequate annotations or notes that include:
    1. How the vessel is physically attached to the test apparatus.
    2. Which load or force transducers and how they are coupled to the vessel.
    3. How strain or displacement is measured.
    4. How the physiological condition of the vessel (e.g. temperature, ionic and osmotic conditions, oxygenation) is maintained during testing.
    5. Include relevant dimensions.
    6. If your design is based on one or more designs or apparatuses found in literature, you must cite the sources and explain how your design is different from them.
  3. Explain with equations how the output of each transducer or measurement device is used to compute the relevant stresses and strains in the vessel. If some required variables can not be directly measured, explain what approximations you make. Remember to state any simplifying assumptions you make in your calculations.
  4. Summarize key relevant specifications of each transducer such as resolution, sensitivity or full-scale deflection.

    1. You do not need to specify the specific transducer model or type or how its electrical outputs are amplified or digitized, but you should propose to use a type of transducer that actually exists. In general this means you will need separate devices that measure either forces or pressures and a separate way of measuring strains such as a camera.
    2. To estimate some of these specifications, perform a finite element analysis with Continuity of simultaneous inflation, stretch and twist of an artery with the dimensions and constitutive properties of your chosen artery type. Explain your choice of maximum inflation, stretch and twisting loads. Don't go too large or the results will be unphysiological and the solutions may not converge. You will probably find it easiest to prescribe the stretch displacement, twist per unit length, and pressure load and then solve for the axial stress, torsional shear stress and radial inflation. But it is possible to prescribe different boundary conditions depending what you want to solve for.

    3. Use applied or computed stresses or force resultants (negative of the residuals) to estimate axial forces and torsional moments. Use these results to help specify requirements for your transducers.
    4. Summarize your model results. Do they seem correct? Can you check them? If you think they are not reliable, explain why and what you might need to change. Are there other useful insights for your design that came out of the model analysis?