2012 Proceedings - International Tissue Elasticity Conference

34
Session POS: Posters
Tuesday, October 2 5:00P – 6:00P
(For Viewing and Discussion through Friday, October 5, 4:15P)
001 MEASURING STRAIN USING THE INVERSE SQUARE RELATION OF RADIATION INTENSITY
AND DISTANCE.
Tareq Alrefae 1 .
1 Kuwait University, Khaldia, KUWAIT.
Background: Strain is an important quantity in determining elasticity of materials. Knowledge of the
amount of elongation or shortening of materials provides key markers that help in assessing its intactness
and viability. In addition to being widely available, techniques for strain measurements are diverse in the
detection methods of materials’ elongation or shortening. For example, elastography, which is applied in
biomedical applications, utilizes sonogram techniques in determining strain measurements [1]. Another
example is that of strain gages which rely on the sensitivity of electrical properties to change in length.
Strain gages are commonly used in mechanical applications [2]. More examples are found in the literature
[2]. To further enrich the library of strain measurement techniques, this work presents a simple method
that relies on basic radiation measurements. Specifically, the presented method utilizes the inverse square
relation of radiation intensity (I) and distance. When this relation is paired with the normal strain (ε)
equation, it becomes easy to theoretically relate strain and radiation intensity, resulting in Equation 1.
Equation 1
Aims: The goal of this work is to develop a simple method to measure strain using the inverse square
relation of radiation intensity and distance [3].
Methods: The set–up in Figure 1 is arranged with an NaI(Tl) detector (Canberra, USA) and an elastic
band as the sample. One end of the elastic band is hooked to a stationary rod, while the other is hooked
to a moveable rod. A 137 Cs point source is attached to the moveable rod. Both rods are assembled on a
bench equipped with a scale that shows the distance between the rods. To measure the angles θ1 and θ2
in Figure 1, a long–arm protractor is used. To accommodate for the geometry of the set–up, Equation 1 is
modified to the following relation:
Equation 2
Results: Figure 2 shows a plot of the strain values obtained from the proposed technique (εr) versus
strain values taken from the bench scale (εa). Ideally, the plot should present a straight line with a slope
of unity and a zero y–intercept. The plot, however, deviates from the ideal values. The main reason for
such deviation is the stochastic nature of radioactive decay. Overcoming this source of error is achievable
by prolonging the dwell time of radiation measurement.
Conclusions: A simple technique is presented to measure strain. This technique, which involves basic
radioactivity measurements, is based on the fundamental inverse square relation of radiation intensity
and distance. The stochastic nature of radioactive decay poses the main source of error. Overcoming this
discrepancy is achieved by prolonging the dwell time of radiation measurement.
References:
[1] Ophir J, Cespedes I, Ponnekanti H, Yazdi Y, Li X: Elastography: A Quantitative Method for Imaging the Elasticity
of Biological Tissues. Ultrason Imaging, 13, pp. 111–34, 1991.
[2] Bower AF: Applied Mechanics of Solids. CRS Press, Boca Raton, FL, USA, 2010.
[3] Knoll GF: Radiation Detection and Measurement. Wiley, New York, NY, USA, 2000.
Figure 1: Experimental set–up.
Figure 2: Strain values obtained from the
proposed technique (εr), versus
strain values taken from the
bench scale (εa).
indicates Presenter