Laboratory 3: Viscoelastic Characterization of Tendon using Harmonic Oscillations November 8/9, 2006 BIOEN 5201 Introduction to Biomechanics Instructor: Jeff Weiss TA: Heath Henninger Lab Quiz: A 10 point lab quiz will be given at the beginning of lab (10% of the lab report grade). Be familiar with the entire protocol EXCEPT suggested steps for data analysis. Please contact Heath if you have ANY questions. Background: Materials are often defined as either being elastic (solid) or viscous (fluid). Certain materials have both solid and fluid attributes and are therefore described as being viscoelastic. A viscoelastic material exhibits the following material behaviors: hysteresis during loading and unloading, creep at constant stress, stress relaxation at constant strain, and stress dependence on strain-rate as well as strain. For example, plastic is an example of a viscoelastic material, and creep is the reason a plastic bag full of precious groceries may give way on your walk home from Smiths. Solid phase viscoelasticity in biological soft-tissue is due to the rearrangement of tissue components at the molecular or micro structural level. Ligament and tendon are examples of soft-tissue that exhibit solid phase viscoelastic properties. Characterizing the stress-strain relationship of a viscoelastic material is a requirement to modeling the time dependence of material behavior, which provides insight to tissue functionality and failure modes. One method for modeling viscoelastic behavior is with harmonic oscillations. Harmonic oscillation tests afford information on time-dependent stress-strain functions. These tests are useful in understanding how strain and strain-rate affect tissue stress, as many physiological activities and most injuries occur at high speeds. One method of reducing or eliminating viscous effects is to run experiments at low strain rates homogenously in a material. Objective: The objective of this laboratory is to determine the viscoelastic material properties of bovine tendon using harmonic oscillations at different frequencies with the mini-materials test machine. NOTE To improve the TA to class ratio, two groups will perform this experiment at one time. Group times are listed on the class website. Equipment required (each test station): 1 mini materials test machine, stop protected. 1 PC with NI A/D card and NI motor controller card, NI Labview software 1 1000 gram load cell (Sensotec, waterproof) with adapters to mount below clamps 1 set tissue clamps and associated mounting hardware 1 set Allen wrenches Digital calipers 0.9% normal saline in misting bottle CD-R of USB for data backup Fig 1: Test sample between clamps. 1 of 6
Experimental procedure: Load Cell Calibration NOTE BE EXTREMELY CAREFUL WITH THE LOAD CELL! IT CAN EASILY BE DESTROYED VIA OVERLOADING or APPLYING TOO MUCH TORQUE WHEN MOUNTING. Load cell calibration enter the load cell calibration factor (grams) in the Labview VI based on the calibration page provided with the load cell from the manufacturer (excitation used here is 2.5 volts), as you did in the previous lab. Calculating the Load Calibration Technique 1 A. The certificate of calibration from the Load Cell company (Sensotec) is required. See the calibration spreadsheet provided at your lab station. B. Find what the load cell output is at maximum load (Fig. 3) Example: Calibrated at: 1000 g Excitation: 5VDC Calibration factor: 37.7171 mv/ V This means: excitation of 37.7171 mv/v at 1000g. C. Load cell amplifier is set to give 2.5V excitation, multiply the load cell output by 2.5V (37.7171 mv/v * 2.5 V = 94.29 mv) D. Next, multiply by the gain. (Gain Fixed at 100X, so 94.29 mv * 100 = 9429 mv = 9.429 V) E. Since the Load is proportional to Voltage, the Force will be proportional to Voltage as well (F α V) and therefore F=k*V. So, we need to find the constant (k). k=f/v=m*g/v Calculate k from this equation. (1000g = 1kg; k=(1 kg * 9.81 m/s^2)/ 9.429V = 1.040. Calculating the Load Calibration Technique 2 A. Hang 3-5 weights on the load cell. B. Plot voltage versus load C. Fit the line, convert slope to N/V. Use for calibration. This value is put into the Load Cal box, to convert the voltage into a force (Newtons). Check the load cell calibration using the lab3_loadmonitor.vi. Enter the N/V calibration in the Cal Load box and hang weights from the load cell to determine how well the load is predicted on the VI. NOTE: if your amplifier does not allow you to zero the starting load, subtract a known baseline zero from the data prior to reporting the results. 2 of 6
Sample Preparation Harvest a ~30 mm length section of the tendon to use as the test sample. Now use the Max Automation Motion controller window to position the load cell clamp in such a way that it is almost parallel to the other clamp fastened to the base. Be careful as you move down the crosshead with the load cell, DO NOT CRASH THE LOAD CELL INTO THE BASE OF THE FIXTURE. On the Motor positioning window, select the appropriate controller card (1-D Interactive), select Relative position and enter a low velocity value for the crosshead. (About 10 is a safe value). Move the motor by about 200 encoder counts at a time for fine positioning. Entering a positive value moves the clamp down and a negative value moves it up. a. Pull up on the Emergency Stop button to release the safety interlock b. Initialize the motor in the Max Automation window i. Highlight PCI-7344 and click Initialize c. Enter a velocity, target position, click Reset Position and click Apply d. Click Start to initiate motion e. Always keep a hand on the Emergency Stop button and press it should unexpected motion occur. Align the base clamp with the load cell clamp by moving the X-Y table plates. Be sure to fasten them tightly in place once they clamps are aligned. Mount sample in tissue clamps so that the region in the x-y plane between the clamps will be nearly square. Move the upper clamp as needed. The tissue should not be pulled tight at this time as there will be a little slack from tightening the clamps. Material Testing Step 1: Tare load application. The objective of this step is to establish the initial zero-load length, and the triangular oscillations align the fibers of the sample. Adjust the load cell balance so that the output is 0 volts. Use the lab3_pre-load.vi to determine an initial zero-load length for the sample. Find a very small displacement value sufficient to load the sample by 0.5 Newtons typically this will be around 1% or less of the sample length. Enter the following values into lab3_pre-load.vi : Preload (N): 0.5 Cal Load (N/V): from your calibration Total Displacement (mm): 5.00 Strain rate (counts/sec): 100 File Path: C:\bioen-5201/lab3\group#-preload.vi Execute the preload.vi: a. Click the arrow in the upper right of the lab3_pre-load.vi to initialize the program i. A green light in the program window will reset b. Press the Start button in the middle of the VI Now cycle the sample through about 10 cycles of triangle waves with a small amplitude using the lab3_tareload.vi. Enter the following values into lab3_tareload.vi : Ligament length clamp to clamp: your measured length Strain %: 1.00 Cal Load (N/V): from your calibration Strain rate: 0.01 File Path: C:\bioen-5201/lab3\group#-tareload.vi 3 of 6
Execute the tareload: a. Click the arrow in the upper right of the lab3_tareload.vi to initialize the program i. A green light in the program window will reset b. Press the Start button in the middle of the VI Move the crosshead down approximately 500 counts to provide definite laxity After the tare load is applied, the tendon is likely to become more lax than before. Adjust the zero length again using the lab3_pre-load.vi. In the lab3_pre-load.vi window, estimate the amount of time the load vs. time graph ramped steeply, then estimate the distance moved during that same time in the position vs. time graph. Convert that distance to actuator counts using the conversion factor in the window (0.001250 mm/ct). Move the cross head down in the Max Automation window with the calculated value as the new Target Position. REMEMBER, POSITIVE IS DOWN, NEGATIVE IS UP. Enter new Target Position Click Reset Position and click Apply Click Start to initiate motion This allows the strain to start from an accurate zero-load length After the true zero-load length is established, measure the distance between the clamp edges (the sample length l 0 to be used in calculating the needed clamp displacement based on desired strains) using digital calipers. Step 2: Preconditioning. The objective of this step is to precondition the material to a strain as large as the maximum strain used in the harmonic oscillation test. If this step was not performed, the max strain used during the harmonic oscillation test would stretch out the material and the force response would become inaccurate due to laxity. Determine the amount of actuator displacement necessary to generate a clamp-to-clamp uniaxial tensile strain of 12%. [(final length-initial length)/(initial length) * 100 = 12] Precondition the sample by determining the displacement required to stretch the sample by 12% using lab3_precondition.vi. Use a slow velocity profile of about 1 count/second, to move the sample from the neutral state to a 12% strain level. Retain at this stretched state for 5 minutes. Enter the following values into the VI: Total displacement (mm): (only the change in length, not final length) Cal Load (N/V): from your calibration Strain rate: 10 counts/sec Scan rate: 20 Hz File Path: C:\bioen-5201/lab3\group#-precondition.vi Execute the tareload: a. Click the arrow in the upper right of the lab3_tareload.vi to initialize the program ii. A green light in the program window will reset b. Press the Start button in the middle of the VI After the 5 minutes under strain, convert the 12% strain distance into encoder counts based on the values provided (0.001250 mm/ct). Using the Max Automation controller, move the sample back slightly past the zero load position (ask TA for help to ensure this value is entered properly). Let the specimen recover in a slightly lax state for 5 minutes. Re-establish and re-measure the zero-load length using the lab3_pre-load.vi. In the lab3_pre-load.vi window, estimate the amount of time the load vs. time graph ramped steeply, then estimate the distance moved during that same time in the position vs. time graph. Convert that distance to actuator counts using the conversion factor in the window (-0.001250 4 of 6
mm/ct). Move the cross head in the Max Automation window with the calculated value as the new Target Position. REMEMBER, POSITIVE IS DOWN, NEGATIVE IS UP. Enter new Target Position Click Reset Position and click Apply Click Start to initiate motion This allows the strain to start from an accurate zero-load length This may be longer than before preconditioning. Balance the load cell using lab3_loadmonitor.vi. Measure the new zero-load length from clamp to clamp. Step 3: Harmonic Oscillation. The objective of this step is to characterize the material by running harmonic oscillations at different strain levels and frequencies. Measure dimensions at the narrowest point (hopefully near the center of the sample) three times using digital calipers (width, thickness). Balance the load cell using lab3_loadmonitor.vi. Using the new zero-load length, determine the amount of actuator displacement necessary to generate uniaxial tensile strains of 4, 8 and 12%. IF THE LOAD CELL SATURATED AT 12% DURING PRECONDITIONING, USE A LOWER SET OF STRAINS (3, 6, 9 OR 2, 4, 6% BASED ON THE PRECONDITIONING LEVEL. Exceeding the preconditioning strain level will result in laxity during the test that will interfere with results. Enter the necessary parameters in the lab3_harmonic_oscillation.vi begin the stress relaxation and cyclic tests. Ligament length (mm): clamp to clamp at new zero-load length Amplitude (%): 1.0 # cycles per frequency: 15 Pre-strain 1, 2, 3: 4, 8, 12 or 3, 6, 9 or 2, 4, 6 based on preconditioning levels Relaxation time 1, 2, 3 (min): 5, 5, 5 Frequency 1, 2, 3, 4 (Hz): 0.5, 1, 3, 5 Load Cal Factor (N/V): from your calibration File path: C:\bioen-5201/lab3\group#-harmonic.vi Click New File/Append File so New File appears Perform the test sequence, with each stress relaxation test following by sinusoidal cyclic testing at frequencies of 0.5, 1.0, 3.0 and 5.0 Hz. Wait for the green light labeled Motion Complete before interrupting the cycle. Ask TA if you are unsure. Back up load-time and actuator displacement-time data onto CD-R/USB before leaving the laboratory. 5 of 6
Data analysis: The objective of the data analysis is to determine both the equilibrium stress-strain response of the tendon and the response to harmonic oscillations. Equilibrium stress-strain behavior: Determine the stress values that correspond to the applied strain at the end of each stress relaxation experiment (at 4%, 8% and 12% strain). Using these three points and the point (0,0), plot the equilibrium stress-strain curve for the tendon. Reduced relaxation curves: Using the data obtained during the relaxation testing, plot the reduced relaxation function corresponding to the relaxation data obtained at each equilibrium strain level. The plot should have log(time) on the x-axis and the value of the reduced relaxation function (linear scale) on the y-axis for all three datasets. Dynamic stiffness and phase angle as a function of frequency and equilibrium strain: Make plots of the dynamic stiffness and phase angle as a function of log(frequency) in radians on the x-axis. The y- axis for the dynamic stiffness graph should be log, while the y-axis of the phase angle graph should be linear. You will need to comment on each of the above graphs in terms of its implications for the material s elastic and viscoelastic behavior. Lab report format: Follow the guidelines for Lab 1 when preparing your laboratory report. Please also include your group ID (i.e. w1, w2, h3...). Suggested steps for data analysis: Use Matlab to first split the data into three segments each consisting of the DC strain application, the stress relaxation segment followed by the harmonic oscillations. Remove the zeroes from your displacement data. Plot this in Excel to determine the points of interest at each strain level. You can supply Matlab with the indices for the points in the sinusoidal segment which you want to separate out of the remaining data for curve fitting. The oscillatory strain input was a sine wave and the expected output of the stress waveform is a sine wave of the same frequency as the input, but out of phase with the input. You will need to analyze this relationship for all the four frequencies at all the three strain levels. This part of the analysis can be done by fitting a sine wave to the strain and stress data as outlined in the class notes on viscoelasticity. Use the last three sine waves of each frequency to do this curve fit. Calculate values of dynamic stiffness and phase shift and generate required plots. 6 of 6