Researchers developed an apparatus to conduct tensile strength tests on swim bladder tissues to obtain biomechanical data. This data could be used to create models for predicting fish susceptibility to barotrauma. The apparatus was tested by conducting tension tests on rubber balloon samples. Three mathematical models - the kinetic theory model, Mooney-Rivlin theory model, and Ogden model - were fitted to the balloon data. The models accurately described the non-linear behavior of the biological material. Validation tests showed the models could also predict the inflation pressure of the balloons. The approach shows promise for evaluating barotrauma susceptibility across different fish species.

1. NEW APPROACH TO EVALUATE
BAROTRAUMA SUSCEPTIBILITY IN FISH
Bernardo Beirão, Luiz G. M. Silva, Ricardo Falcão
bvbeirao@gmail.com
Federal University of São João del-Rei – UFSJ, Brazil
American Fisheries Society
145th Annual Meeting – Portland, OR

2. Fonte: ANEEL, 2012
About 1,000 power
plants already installed
which corresponds to
76% of the electrical
energy generation
It corresponds to only
~30% of the inventoried
hydropower capacity
American Fisheries Society
145th Annual Meeting – Portland, OR

3. Fonte: ANEEL, 2012
Amazon River Basin
Higher diversity
Larger fish
American Fisheries Society
145th Annual Meeting – Portland, OR
Facilities concentrated in
the South, Southeast
and Center-West

4. American Fisheries Society
145th Annual Meeting – Portland, OR
Courtesy:RichBrown

5. Courtesy:RichBrown
American Fisheries Society
145th Annual Meeting – Portland, OR

6. Swim Bladder Rupture
Exophthalmia
Stomach or Intestine Eversion
Hemorrhage
Emboli
BROWN, R.S.
BROWN,R.S.
ALVES, C.B.M.
American Fisheries Society
145th Annual Meeting – Portland, OR

7. Brown et al. (2014)
American Fisheries Society
145th Annual Meeting – Portland, OR

8. Biomechanical information about swim bladder structure can
provide data to create barotrauma susceptibility prediction models
- Construction of an apparatus to realize tensile strength
tests with swim bladder tissues
- Apparatus commissioning with rubber balloons samples
Assumptions: Isotropic – Incompressible - Spherical
V = V0
American Fisheries Society
145th Annual Meeting – Portland, OR

9. Force Sensor
Tested Sample
Moving Cart
Arduino
American Fisheries Society
145th Annual Meeting – Portland, OR

10. Symbol Description Size (mm)
W Initial width of the narrow area 2,1
WO Total width 4,8
Wc Central width of the narrow area 1,4
L Length of the narrow area 6,3
LO Total length 30,0
G Length of the tearing area 5,4
D Distance of the narrowing sections 12,7
T Thickness 0,35
R Internal radius 3,5
RO External radius 6,3
ASTMInternational
American Fisheries Society
145th Annual Meeting – Portland, OR

11. Trials
Logger Pro v. 3.6.1
American Fisheries Society
145th Annual Meeting – Portland, OR

12. - Models calculated:
- Kinetic theory model
- Mooney-Rivlin theory model
- Ogden model
Related to elastic materials
Used in biology modeling research
American Fisheries Society
145th Annual Meeting – Portland, OR

13. Model equations for the tension tests
Adapted from Mueller & Strehlow, 2004
𝐹𝐹 = 𝑊𝑊0 � 𝑇𝑇0 � 𝑠𝑠+ 𝛽𝛽 − 𝛽𝛽−5
Adapted from Mueller & Strehlow, 2004
𝐹𝐹 = 𝑊𝑊0 � 𝑇𝑇0 𝑠𝑠+ 𝛽𝛽 − 𝛽𝛽−5 + 𝑠𝑠− 𝛽𝛽−3 − 𝛽𝛽3
𝐹𝐹 = 𝑊𝑊0 � 𝑇𝑇0 �
𝑝𝑝=1
𝑁𝑁
𝜇𝜇𝑝𝑝 𝛽𝛽 𝛼𝛼𝑝𝑝−1
− 𝛽𝛽−2𝛼𝛼𝑝𝑝−1
Adapted from Ogden, 1984
- Ogden Model
- Mooney-Rivlin Theory Model
- Kinetic Theory Model
𝛽𝛽 =
𝐿𝐿
𝐿𝐿0
American Fisheries Society
145th Annual Meeting – Portland, OR

14. The data calculated by the model is, then, inserted into the
correspondent pressure model, allowing to predict the maximum
pressure that material can hold;
To verify whether the model responded to what was expected, the
balloon was filled up with air whilst the pressure was measured.
American Fisheries Society
145th Annual Meeting – Portland, OR

15. Inflation tests
American Fisheries Society
145th Annual Meeting – Portland, OR

16. 𝑝𝑝 = 2
𝑡𝑡0
𝑟𝑟0
� 𝑠𝑠+ 𝛽𝛽−1 − 𝛽𝛽−7
𝑝𝑝 = 2
𝑡𝑡0
𝑟𝑟0
𝑠𝑠+ 𝛽𝛽−1 − 𝛽𝛽−7 + 𝑠𝑠− 𝛽𝛽−5 − 𝛽𝛽
𝑝𝑝 = 2
𝑡𝑡0
𝑟𝑟0
�
𝑝𝑝=1
𝑁𝑁
𝜇𝜇𝑝𝑝 𝛽𝛽 𝛼𝛼𝑝𝑝−1
− 𝛽𝛽−2𝛼𝛼𝑝𝑝−1
𝛽𝛽 =
𝑟𝑟
𝑟𝑟0
American Fisheries Society
145th Annual Meeting – Portland, OR
Inflation tests
- Ogden Model
- Mooney-Rivlin Theory Model
- Kinectic Theory Model
Adapted from Mueller & Strehlow, 2004
Adapted from Mueller & Strehlow, 2004
Adapted from Ogden, 1984

17. Apparatus commissioning
- Kinetic Theory
𝐹𝐹 = 6 � 10−7
� 300000 𝛽𝛽 − 𝛽𝛽−5
American Fisheries Society
145th Annual Meeting – Portland, OR
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
Force(N)
β(L/L0
)

18. The balloon showed an non-linear behavior, as expected
for biological materials (Lapeer et al., 2011; Ribeiro et al.,
2012).
American Fisheries Society
145th Annual Meeting – Portland, OR
0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
Force(N)
β(L/L0
)

19. Model Validation
- Kinetic Theory
𝑝𝑝 = 2 � 0,025 � 𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑 𝛽𝛽−1
− 𝛽𝛽−7
American Fisheries Society
145th Annual Meeting – Portland, OR

20. Didn’t explain well, but gives good notion on thermodynamics of
the material (Mueller & Strehlow, 2004)
American Fisheries Society
145th Annual Meeting – Portland, OR

21. 𝐹𝐹 = 6 � 10−7
� 300000 𝛽𝛽 − 𝛽𝛽−5
+ 30000 𝛽𝛽−3
− 𝛽𝛽3
American Fisheries Society
145th Annual Meeting – Portland, OR
Apparatus commissioning
- Mooney-Rivlin Theory

22. 𝑝𝑝 = 2 � 0,025 300000 𝛽𝛽−1
− 𝛽𝛽−7
+ 30000 𝛽𝛽−5
− 𝛽𝛽
American Fisheries Society
145th Annual Meeting – Portland, OR
Model Validation
- Mooney-Rivlin Theory

23. 𝐹𝐹 = 6 � 10−7
� 300000 𝛽𝛽2−1
− 𝛽𝛽 −2�2 −1
+ 𝟏𝟏𝟏𝟏, 𝟐𝟐𝟐𝟐 𝛽𝛽𝟔𝟔,𝟒𝟒𝟒𝟒−1
− 𝛽𝛽 −2�𝟔𝟔,𝟒𝟒𝟒𝟒 −1
American Fisheries Society
145th Annual Meeting – Portland, OR
Apparatus commissioning
- Ogden Model

24. 𝑝𝑝 = 2 � 0,029 300000 𝛽𝛽2−3
− 𝛽𝛽 −2�2 −3
+ 𝟏𝟏𝟏𝟏, 𝟐𝟐𝟐𝟐 𝛽𝛽𝟔𝟔,𝟒𝟒𝟒𝟒−3
− 𝛽𝛽 −2�𝟔𝟔,𝟒𝟒𝟒𝟒 −3
American Fisheries Society
145th Annual Meeting – Portland, OR
Model Validation
- Ogden Model

25. American Fisheries Society
145th Annual Meeting – Portland, OR
Variable Fixed values (a)
d0 4,0 x 10-4 m
r0 1,4 x 10-2 m
μ1 300.000 Pa
μ2 18,22 Pa
α1 2
α2 6,48
Variable Fitted Model (b)
d0 4,0 x 10-4 m -
r0 1,4 x 10-2 m -
μ1 300.000 Pa -
μ2 38,86 Pa ± 39,00
α1 2 -
α2 6,25 ± 0,43

26. Assumptions: Isotropic – Incompressible - Spherical
V = V0
American Fisheries Society
145th Annual Meeting – Portland, OR
Biological materials Vs. Elastic materials
Mechanical properties

27. • Balloon tests provided good results for a initial stage
• Improvements are already being done based on these tests
It is possible to come up with new methodologies to test a
large number of fish types and come up with a realistic
metric for determining barotrauma in different countries
American Fisheries Society
145th Annual Meeting – Portland, OR

28. American Fisheries Society
145th Annual Meeting – Portland, OR

29. American Fisheries Society
145th Annual Meeting – Portland, OR

30. - Prof. Dr. Carlos Martinez – CPH/UFMG
- Prof. Dr. Edson Dias, Natália Castelo Branco, Luma,
Sarah, Aline Assunção & Nathalia Stockler – UFSJ
- Emily Anderson, Rich Brown, Alison Colotelo &
Stephanie Liss – Pacific Northwest National Laboratory
- Ricardo Walker – US Army Corps of Engineers
CPH
American Fisheries Society
145th Annual Meeting – Portland, OR