=Paper=
{{Paper
|id=Vol-1730/p08
|storemode=property
|title=Realization of the Control Software of the Rheometer for Viscoelastic Tests on Articular Cartilage
|pdfUrl=https://ceur-ws.org/Vol-1730/p08.pdf
|volume=Vol-1730
|authors=Guido Giuseppe Garozzo
|dblpUrl=https://dblp.org/rec/conf/system/Garozzo16
}}
==Realization of the Control Software of the Rheometer for Viscoelastic Tests on Articular Cartilage==
https://ceur-ws.org/Vol-1730/p08.pdf
Realization of the Control Software of the
Rheometer for Viscoelastic Tests on Articular
Cartilage
Guido Giuseppe Garozzo
University of Catania
Department of Elettics, Elettronics and Informatics Engineering
Viale A.Doria 6, 95125, Catania, Italy
Email: guido.garozzo@studium.unict.it
Abstract—The Control software developed in LabVIEW was measured. The functional principle of rotational rheometers
realized for an instrument for the measurement of viscoelastic consists in rotating a plate at a given speed, by a motor, to
parameters of the articular cartilage in a humid environment, apply the rotational movement to specimen among the two
in particular, for the measurement of the complex modulus G
and the loss coefficient tanδ, as a function of the frequency and plates. From the measurement of the torque can be gained the
the applied pressure. The rheometer is capable of applying a tension of the specimen and the speed of the applied shear
controlled displacement of between 10% and 30% of the height gradient. In parallel- plates rheometers the shear gradient
of the same sample, and a rotation on the plane of the specimen
of 5 to 15 degree in a frequency range of 0.01 Hz and 2 Hz. The Ωr
γ̇ = (1)
tests were carried out initially on semifluid silicone specimens, to h
test and calibrate the equipment; then, on specimens of cartilage
and sub-chondral bone immersed in saline solution. The tests
varies with the radius. The torque can be written in terms of
carried out have shown the module and phase values of G in the shear stress integral:
good agreement with those found in the literature, proving the Z R Z R
effectiveness of the software by reducing the measurement error M= σr(2πr)dr = η γ̇r(2πr)dr
at the lowest possible. 0 0
Keywords: Rheomoter, Articular Cartilage, LabVIEW, Viscoelas- Z R (2)
2πΩη 3 πΩηR4
tic, Complex Modulus = r dr =
h 0 2h
I. I NTRODUCTION
from which one can derive the equation of rheometer:
The study of the viscoelastic properties arises from the
need to derive the dynamic behavior of certain materials; for 2M h
η= (3)
this purpose we use instruments named Rheometers. These πR4 Ω
instruments were born to study viscous or non-Newtonian For the simplicity of use, the parallel-plates rheometers are
fluids. Today, however, it also makes great use to characterize widely used to do measurement of viscoelastic properties. Aim
the viscoelastic properties of synthetic and biological materials of this work is to realize a low cost parallel-plates strain-
[1]–[5]. Generally, a rheometric test consists in measuring a controlled rheometer to measure the parameters of articular
dynamic variable (force, torque, pressure) and a kinematic cartilage [6]–[8]. The cartilage is a particular type of connec-
variable (velocity, displacement). There are various types of tive tissue characterized by resistance and elasticity. It plays
rheometers that can be classified according to the motion a role of structural support within the body and its composed
typology. These may be in rotational flow (closed trajectory) of cells dispersed in an abundant extracellular matrix, rich in
or in a non- rotational flow (open trajectory). The motion fiber and amorphous substance of protein origin. The articular
can occur by sliding between two surfaces, which can be in cartilage is a layer of low friction bearing soft tissue that
parallel planes, coaxial cylinders, cone-plate, parallel plates. overlaps the articular bone ends in the junctions [9]–[12].
The easiest way to study a material with a rheometer is to The ability of articular cartilage to withstand high compressive
allow the fluid to move according to trajectories closed, ie loads without being damaged is due to the multiphase nature of
repeated indefinitely in time. This principle is realized in the the tissue. The particular composition of the articular cartilage
rotational rheometers. These can be stress-controlled, where (AC) gives to it the viscoelastic properties, in fact the we can
the torque it imposed and the rotation is measured, or strain- distinguish three phases: a ”Solid phase” composed mainly of
controlled, where the rotation it imposed and the torque is collagen fibers and macromolecules of PG tied to chains of
hyaluronic acid; a ”Fluid phase” mainly composed of water;
Copyright c 2016 held by the author. an ”Ionic phase” composed of electrolytes dissolved in water
with both negative and positive charge. These three phases act
45
together to create a tissue capable of bearing huge compression 1067-0 Phidgets Stepper Bipolar Phidget-HC, which allows
stress and the associated shear. The interstitial fluids of the you to control its position, velocity and acceleration. For
AC are composed from the fluid and ionic phase. The AC is measuring of the force, a load cell Laumas 150 N was used,
presented as a layered structure with three layer [5], [13]: with a NI DAQ 6008 acquisition card as a signal amplifier
• Superficial Layer: with the major quantities of water and and a further signal amplifier (Transducer Techniques BMT-
collagen’s fibrils; 01). The stepper motor and the actuator are connected to
• Middle Layer: with quantities of water and collagen’s the controller and this, through the USB port, to the control
fibrils less than the superficial layer; and processing system. The rheometer is made of a frame of
• Deep layer: divided in two zones (Deep zone and Calci- metal sections, anchored to a base on which have been fixed
fied zone) where quantities of water and collagen’s fibrils the motor control board, the acquisition card and the signal
are constant and the PG have the maximum concentration. amplifier. A custom-made threaded joint transmits the rotate
motion to the cartilage. A vessel contains the cork lower disc,
II. D ESIGN AND CREATION OF THE R HEOMETER the cartilage and the saline solution for moist tests. On the
To determine the dynamic viscoelastic response must submit upper crossbar was made a guide (with steel laminations and
the specimen to a condition of deformation that does not a bearing SKF [16]) for the load cell, in order to translate it
involve a change in volume nor a shift of interstitial fluid vertically. An upper compression plate was installed under the
[10]. By applying a sinusoidal torque Mt (t), the specimen load cell. This consist of an assembly of screw- bearing-cork’s
will respond with a sinusoidal angular deformation γ but with plate. The last has truncated cone shape. This system has two
a delay δ, functions: to transmit the vertical load of the linear actuator
( for compressing, and sending the response of the simple to the
Mt (t) = Mt sin(ωt) ⇒ τ = τ0 sin(ωt) torsion measurement system. The upper cork’s plate, in fact,
(4)
(t) = sin(ωt + δ) ⇒ γ = γ0 sin(ωt + δ) was vertically carved on one side to accommodate a very thin
(0.5 mm) and flexible plate of plastic material (Plasticard).
where τ is the shear stress. The dynamic shear modulus or
This is made with strain gauge (Fig. 2). The stepper motor
complex modulus G∗ is defined by:
and the actuator used, both have a step- by-step technology
τ τ0 and have the same electrical characteristics, therefore, it was
= G∗ = G0 + iG” = (cos(δ) − i sin(δ)) (5)
γ γ0 chosen a single controller with a sensitivity of 1/16 step, which
activates one or other by means of a switch. A computer, with
τ0
|G∗ | = (6) a software developed in NI LabVIEW, has allowed operating
γ0 the machine and elaborating its measurements. A simulation
with the elastic modulus G’ and the viscous modulus G”. software was created for laying the foundations to what later
To achieve the goal of measuring the viscoelastic properties, will be the final software. In this was considered the lower
the measurement was made at different frequencies with a disc in the form of sine wave generator and the sample as a
rotational rheometer made in lab. The design of the rheometer simple band pass filter, since the viscoelastic behavior has a
was done with the software SolidW orkstm (Fig. 1a). This frequency response similar.
rheometer is divided in two parts: an Upper part with the
actuator and the load cell and a Bottom part with the stepper III. S OFTWARE IMPLEMENTATION
motor and the test chamber. The rheometer is controlled from a notebook with the
The rheometer was built following the design (Fig. 1b), control software (CS) created in the development environment
and to keep the correct operation of the machine it was NI LabV IEW tm . The CS enables to make the measures
necessary to create the joints with bearings specifically for totally automated. The peripherals needed to execute this task
that purpose. The equipment is constituted of a metal frame are: the NI DAQ 6009 used to read data from the load cell;
with two crossbars. The upper part is connected the specimen a NI SCXI Chassis with NI SCXI 1520 plug-in to read the
compression system, in series to the load cell and to the strain gauge data. At first, the CS applies compression to the
upper compression plate. The lower crossbar supports, instead, specimen with the actuator and, after reaching a given force,
the system of rotation, connected to the lower plate. The the stepper start to impose the sinusoidal angular deformation.
plates, together with the simple, are immersed in a plastic The shear stress was measured by a custom-made load cell
can, which contains a physiological solution, to performing with a strain gauge mounted on the Plasticard lamina [14],
the tests on the cartilage in a humid environment. A Robot- [17], [18]. Moreover, the software processes the measured
Italy 39BYGL bipolar stepper motor, equipped with endless data, calculates complex modulus and loss coefficient and ends
screw to convert the rotary motion in a linear one, provides the with the construction of graphs and charts and exporting them
vertical compression. For applying the torque has been used in .xlsx file (Exceltm ). The front panel of the CS is divided in
a bipolar stepper motor Phidgets 3321-0-28STH32 NEMA- sheets; the first one is active at the beginning of the measure
11 with integrated planetary gearbox (Gearbox 27:1). It has process until the compression applied to the specimen ends
a maximum speed of 120 rpm and a nominal torque of 1.4 (Fig. 3). In this sheet is written the description of the measure.
Nm [14], [15]. The stepper motor is connected to a controller The second sheet, active in the oscillation phase of the measure
46
(a) Design (b) Realization
Fig. 1. Design and realization of the Rheometer.
Fig. 5. Feedback control
Fig. 2. Plastic lamina in the instrument the error indicators. The first step of the measure process
consists to apply compression of the specimen until reaching
the desired force. The actuator moves quickly and, when
reaches the sample, the speed is reduced to avoid their over-
compression. The compression is a function of the percentage
of the height of the simple, which is to be compressed. In
practice, in the instant in which it touches the specimen is
applied the percentage of displacement defined. When the
compression is finished, the CS stand by for the equilibrium
time of the simple, usually 300 600 s . At the same time, the
Fig. 3. Starting phase sheet software evaluates the error due to interferences in the strain
measurement system. A flip-flop custom-made in LabVIEW
is used to record the instant of time that the actuator touches
the simple, connecting the stepper driver to the load cell in
closed loop with a feedback control (Fig. 5).
The second step of the measure process is the heart of the CS,
this one imposes the oscillations to the specimen. The number
of oscillation per frequency are usually 5 or 10 because is
needed have the necessary raw data to be processed. In the
last step the acquired Raw data are processed to extract the
Fig. 4. Oscillation phase sheet necessary information to our purpose. This process is needed
to calculate the complex modulus and the loss coefficient
of the tested material (Fig. 6) . The complex modulus is
process, monitors the oscillations applied to the sample and calculated with the equation 6 using labVIEW’s blocks (Fig.
its step-by-step response (Fig. 4). The others sheets contain 7) and the Loss coefficient is calculated with an algorithm
the graphs of the viscoelastic properties of the sample, and that uses the Hilbert transform and other LabVIEW’s blocks
47
Fig. 6. Data processing block
Fig. 10. Exports graphs sample
Fig. 7. Complex modulus algorithm
Fig. 11. Silicone Complex Modulus graph
Fig. 8. δ extraction algorithm in labVIEW
Fig. 12. Silicone Loss Coefficient graph
Fig. 9. Build Graphs block IV. D ISCUSSIONS AND TEST ’ S R ESULTS
Specimens of silicone were used to verify the functionality
to extract the phase delay δ (Fig. 8). of the instrument and during its testing. Figure 11 shows the
In the CS is present the function that allows to record the graph of the silicone module —G *—; the variation of the
numeric data of the complex modulus and the loss coefficient, module is of the order of centimes of MPa, the resulting curve
and their plots in the same file with the fitting’s informations, fitting has as equation:
such as fitting curve and polynomial equations (Fig. 9). The
final data are plotted and recorded, in file .xlsx building a f (x) = 0.425 − 0.185x + 3.233x2
(7)
report file in the CS (Fig. 10). − 8.38x3 + 9.41x4 − 5x5 + 1x6
48
Fig. 15. Frequency-Complex modulus graph
Fig. 13. Articular Cartilage in the test chamber
Fig. 14. Frequency-Loss coefficient graph
The loss coefficient determined by tan(δ) has a negative
variation (Fig. 12); the fitting has as equation:
f (x) = 0.63 − 4.839x + 15.164x2
(8)
− 24.455x3 + 21.245x4 − 9.465x5 + 1.695x6
Fig. 16. Literature plots
Despite the silicone samples had different curing times
and small physical differences, tests produced similar results, were extracted from the data processed by software:
highlighting the reliability of the rheometer in the predeter-
y = −1E − 13x6 + 8E − 11x5 − 2E − 08x4
mined range. Having been checked for good reliability of (9)
the device, the dynamic characteristics of hyaline or joint + 3E − 06x3 − 0, 0002x2 + 0, 0055x + 0, 8096
cartilage samples were evaluated. The specimens used in tests y = 2E − 14x6 − 2E − 11x5 + 6E − 09x4
were extracted from a cow’s knee joint, in particular from the (10)
bottom part of the femur. The specimens were fresh when + 9E − 07x3 + 6E − 05x2 − 0, 0024x + 0, 2518
were used and had characteristics: the 9 is the equation that rappresents the fitting curve of
• 1 mm of cartilage attached to 5 mm of subchondral bone; the complex modulus, the 10 is the fitting’s equation of
• 1 mm of cartilage attached to 1 mm of subchondral bone. the loss coefficient. This test aims to demonstrate that the
energy applied to the AC gives a response that changes,
To begin the test, the specimen is inserted into the test chamber from a prevalently viscous behaviour to a prevalently elastic
full of saline solution (Fig. 13), needed to simulate the real behaviour with the increase of frequency of application of the
condition into the knee joint. The range of frequencies used oscillations.
in tests was 0.01 ÷ 2 Hz. The cartilage was compressed with
a force of about 0.7N and left to relax for about 300 s V. C ONCLUSION
prior to imposing the γ angular deformation. The results were The predetermined objective in this work was the design
satisfactory as comparable with those of the literature. The and realization of a software able to control an instrument, the
graphs of complex module (Fig. 15) and loss coefficient (Fig. rheometer, for evaluate the viscoelastic properties of cartilage
14) as a result of a test. The graphs founded in literature (Fig. or more generally of two-phase materials. The instrument
16) are similar to the graphs that the CS made, so this confirm made has proved able to meet the expectations, providing
that the Software do his job very well. The complex modulus results consistent with those reported in the literature. The
is measured in MPa and the frequency in Hz. A sixth order developed software allows complete control with regard to
equations of the complex modulus and of the loss coefficient the action on the specimen and the analysis of its reactions,
49
thus making it completely self-sufficient machine. In fact [17] E. Pedulla, F. Lo Savio, G. Plotino, N. M. Grande, S. Rapisarda,
the use of advanced soft computing techniques has became G. Gambarini, and G. La Rosa, “Effect of cyclic torsional preloading
on cyclic fatigue resistance of protaper next and mtwo nickel–titanium
progressively an effective option in many contexts [?], [19]– instruments,” Giornale Italiano di Endodonzia, vol. 29, no. 1, pp. 3–8,
[24]. It was created a campaign of tests, both of elastomers that 2015.
of biological tissues, which allowed to calibrate the machine [18] F. Lo Savio, E. Pedullà, E. Rapisarda, and G. La Rosa, “Influence
of heat-treatment on torsional resistance to fracture of nickel-titanium
both from a hardware and software point of view and to verify endodontic instruments,” Procedia Structural Integrity, vol. 2, pp. 1311–
the results which, as mentioned, are consistent with those 1318, 2016.
found in the literature. [19] M. Wozniak, C. Napoli, E. Tramontana, and G. Capizzi, “A multiscale
image compressor with rbfnn and discrete wavelet decomposition,” in
International Joint Conference on Neural Networks (IJCNN). IEEE,
R EFERENCES 2015, pp. 1219–1225.
[1] M. Calı̀ and F. Lo Savio, “Accurate 3d reconstruction of a rubber mem- [20] G. Capizzi, G. Lo Sciuto, C. Napoli, and E. Tramontana, “A multithread
brane inflated during a bulge test to evaluate anisotropy,” in Advances nested neural network architecture to model surface plasmon polaritons
on Mechanics, Design Engineering and Manufacturing. Springer propagation,” Micromachines, vol. 7, no. 7, p. 110, 2016. [Online].
International Publishing, 2017, pp. 1221–1231. Available: http://www.mdpi.com/2072-666X/7/7/110
[2] K. Boettcher, S. Grumbein, U. Winkler, J. Nachtsheim, and O. Lieleg, [21] C. Napoli and E. Tramontana, “Massively parallel wrnn reconstructors
“Adapting a commercial shear rheometer for applications in cartilage for spectrum recovery in astronomical photometrical surveys,” Neural
research,” Review of Scientific Instruments, vol. 85, no. 9, p. 093903, Networks, vol. 83, pp. 42–50.
2014. [22] C. Napoli, G. Pappalardo, M. Tina, and E. Tramontana, “Cooperative
[3] M. R. VanLandingham, N.-K. Chang, P. Drzal, C. C. White, and S.-H. strategy for optimal management of smart grids by wavelet rnns and
Chang, “Viscoelastic characterization of polymers using instrumented cloud computing,” IEEE Transactions on Neural Networks and Learning
indentation. i. quasi-static testing,” Journal of Polymer Science Part B: Systems, vol. 27, no. 8, pp. 1672–1685, 2016.
Polymer Physics, vol. 43, no. 14, pp. 1794–1811, 2005. [23] F. Bonanno, G. Capizzi, and G. Lo Sciuto, “A neuro wavelet-based ap-
[4] M. Calı̀, D. Speranza, and M. Martorelli, “Dynamic spinnaker per- proach for short-term load forecasting in integrated generation systems,”
formance through digital photogrammetry, numerical analysis and ex- in Clean Electrical Power (ICCEP), 2013 International Conference on.
perimental tests,” in Advances on Mechanics, Design Engineering and IEEE, 2013, pp. 772–776.
Manufacturing. Springer, 2017, pp. 585–595. [24] F. Bonanno, G. Capizzi, S. Coco, A. Laudani, and G. Lo Sciuto, “A
[5] V. C. Mow, S. Kuei, W. M. Lai, and C. G. Armstrong, “Biphasic creep coupled design optimization methodology for li-ion batteries in electric
and stress relaxation of articular cartilage in compression: theory and vehicle applications based on fem and neural networks,” in Power
experiments,” Journal of biomechanical engineering, vol. 102, no. 1, pp. Electronics, Electrical Drives, Automation and Motion (SPEEDAM),
73–84, 1980. 2014 International Symposium on. IEEE, 2014, pp. 146–153.
[6] S. Miyata, T. Tateishi, K. Furukawa, and T. Ushida, “Influence of struc- [25] D. Gotleyb, G. Lo Sciuto, C. Napoli, R. Shikler, E. Tramontana, and
ture and composition on dynamic viscoelastic property of cartilaginous M. Woźniak, “Characterisation and modeling of organic solar cells by
tissue: criteria for classification between hyaline cartilage and fibrocarti- using radial basis neural networks,” in International Conference on
lage based on mechanical function,” JSME International Journal Series Artificial Intelligence and Soft Computing. Springer, 2016, pp. 91–
C Mechanical Systems, Machine Elements and Manufacturing, vol. 48, 103.
no. 4, pp. 547–554, 2005.
[7] A. Mak, “The apparent viscoelastic behavior of articular cartilagethe
contributions from the intrinsic matrix viscoelasticity and interstitial fluid
flows,” Journal of biomechanical engineering, vol. 108, no. 2, pp. 123–
130, 1986.
[8] M. Stading and R. Langer, “Mechanical shear properties of cell-polymer
cartilage constructs,” Tissue engineering, vol. 5, no. 3, pp. 241–250,
1999.
[9] S. C. R. Skalak, Handbook of Bioengineering. McGraw Hill, 1986,
ch. 4.
[10] L. Q. Wan, J. Jiang, D. E. Miller, X. E. Guo, V. C. Mow, and H. H.
Lu, “Matrix deposition modulates the viscoelastic shear properties of
hydrogel-based cartilage grafts,” Tissue Engineering Part A, vol. 17, no.
7-8, pp. 1111–1122, 2011.
[11] G. Vunjak-Novakovic and S. Goldstein, “Biomechanical principles of
cartilage and bone tissue engineering,” Basic orthopaedic biomechanics
and mechanobiology, pp. 343–408, 2005.
[12] A. A. Spirt, A. F. Mak, and R. P. Wassell, “Nonlinear viscoelastic prop-
erties of articular cartilage in shear,” Journal of Orthopaedic Research,
vol. 7, no. 1, pp. 43–49, 1989.
[13] D. A. Grande, A. S. Breitbart, J. Mason, C. Paulino, J. Laser, and
R. E. Schwartz, “Cartilage tissue engineering: current limitations and
solutions.” Clinical orthopaedics and related research, vol. 367, pp.
S176–S185, 1999.
[14] G. La Rosa, F. Lo Savio, E. Pedullà, and E. Rapisarda, “Developing of
a new device for static and dynamic tests of ni-ti instruments for root
canal treatment,” Procedia Structural Integrity, vol. 2, pp. 1303–1310,
2016.
[15] E. Pedullà, F. Lo Savio, S. Boninelli, G. Plotino, N. M. Grande,
G. La Rosa, and E. Rapisarda, “Torsional and cyclic fatigue resistance of
a new nickel-titanium instrument manufactured by electrical discharge
machining,” Journal of endodontics, vol. 42, no. 1, pp. 156–159, 2016.
[16] G. Sequenzia, S. Oliveri, M. Calabretta, G. Fatuzzo, and M. Cali, “A
new methodology for calculating and modelling non-linear springs in
the valve train of internal combustion engines,” in SAE Technical Paper.
SAE International, 04 2011.
50