BIOMECHANICS OF THICK, SOFT TISSUE TUBES: ASSESSMENT OF RAT URETHRAS
In my Biomechanics II course junior year of college, we were tasked with the responsibility of assessing how the compliance, incremental elastic modulus, and circumferential stress-strain relationships at inner, midwall, and outer radii of proximal, middle, and distal segments of a female rat urethra specimen in a rat birth trauma model behave with increasing intraluminal pressure. This lab was completed in teams of two.
OBJECTIVE:
Assess the biomechanical properties of a female rat urethra in a rat birth trauma model.
Use MATLAB:
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Average the data for each pressure increment
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Calculate inner diameter (ID) and normalized inner diameter (NID) for each averaged pressure increment
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Using the averages and the theory from the lecture on thick-walled cylinders, calculate and plot the following parameters for each axial location along the soft tissue tube:
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Pressure vs NID
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Compliance for low, middle and high pressure ranges
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Incremental elastic modulus at each pressure
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Circumferential stress vs strain at:
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inner radius
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midwall radius
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outer radius
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Discuss the following issues:
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Differences among the three positions along the length of the tissue tube
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Differences in stress/strain through the thickness
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Possible improvements to the experimental protocol
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Clinical relevance of experiments
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CONCLUSION:
In conclusion, the rat urethra follows distinct trends within each segment due to its nonhomogeneous nature, ultimately identifying key areas contributing to stress urinary incontinence (SUI) due to vaginal distension (VD) post-birth. Further biomechanical and structural analyses of the female rat urethra for a rat birth trauma model are needed to draw specific conclusions on urethral functionality, how each segment affects SUI, and the effect of VD on the urethra. Thus, we hypothesize that since there is a net increase in inner diameter and circumferential strain with increases in intraluminal pressure for proximal, middle, and distal segments of the female rat urethra, VD induces SUI. VD increases the degree of effect SUI has on the urethra with increases in intraluminal pressure.
REPORT SUMMARY
LAB SETUP
Just as in the Prantil et al. paper, a female rat urethra in a rat birth trauma model was placed in a tissue chamber consisting of a 37° circulation loop. This circulation loop mimics body temperature to keep the specimen warm. Oxygen and carbon dioxide were also present in the tissue chamber to keep the specimen alive. A beaker full of water acted as the fluid reservoir or pressure head and was directly attached to the specimen. To remove the urethra from the rat model and place it in the chamber, it had to be cut at both the proximal and distal ends. Once in the tissue chamber, the specimen was capped at the distal end to prevent any fluid loss during experimentation. Capping at the distal end ensured a constant pressure in the specimen by preventing fluid flow throughout experimentation. A laser micrometer was used to measure the outer diameter and thickness of the specimen. The laser micrometer consists of a light source and receptor. The laser was applied to the middle of the specimen. The specimen blocked a certain amount of
of light that was blocked from reaching the receptor was determined by the receptor as the outer diameter of the specimen. An Edwards Life Sciences TruWave Pressure Transducer, with a working range of - 50 to 300mmHg and an accuracy of ±1mmHg, was positioned proximal to the urethra and was used to measure the system pressure. The pressure transducer acts like a Wheatstone bridge with a physical strain gauge that deforms in real time. It outputs a change in voltage value in analog units. A Lab-View Graphing User Interface was also used to graphically display the data gathered from the pressure transducer and laser micrometer in real time. Finally, an analog-to- digital converter was used to convert measured outer diameter and pressure analog units to real world units that would be used for further analysis.
RESULTS & PLOTS
DISCUSSION
Average Normalized Inner Diameter vs. Average Pressure
In reference to Figure 2, the average normalized inner diameter of the proximal segment increased by roughly two times the original, unloaded diameter, whereas the normalized inner diameters of the middle and distal segments stayed relatively similar, with only a slight increase from the unloaded inner diameters. This means that the lumen of the proximal segment of the rat urethra stretched significantly more than the other two segments in response to increasing intraluminal pressure thus indicating a more intense response to inner pressure changes. The middle and distal segments’ normalized inner diameters appear to decrease before they increase in size. This finding is in line with the compliance and strain behavior exhibited in Figures 3 and 5 respectively as they indicate a reduction in radius due to an increase in intraluminal pressure (negative compliance) and compression of the diameter at lower intraluminal pressure (negative strain).
Compliance
In reference to Figure 3, the proximal segment of the female rat urethra has the highest compliance of the three segments at low and middle pressures and the second highest compliance at high pressure. Thus, the proximal segment remains relatively compliant as the intraluminal pressure increases thus aligning with consistent increases in the normalized inner diameter in the proximal segment in Figure 2. With regards to the distal and middle segments, the distal segment
is most pliable during the middle pressure range while the middle segment is most pliable during the high pressure range. These explanations are confirmed by Figure 2. During the middle pressure range (6-12mmHg), the distal and proximal segments experience the largest degree of inner diameter deformation in comparison to the low (0-6mmHg) and high (12-20mmHg) pressure ranges. During the high pressure range (12-20mmHg), the middle segment experiences the largest degree of inner diameter deformation in comparison to the low and middle pressure ranges. Note that both the middle and distal segments have negative compliances at the low pressure range. In theory, a negative compliance corresponds to the radius of the specimen decreasing, or compressing, as the internal pressure increases. In reality, these negative compliance values may be due to noise. The noise created within this interval is different than the noise filtered in MATLAB between pressure intervals; It is filtered at pressure changes, so still the data is displaying noise. This is because the data is from a real, biological sample.
Incremental Elastic Modulus
As discussed in the Results section, there is a considerable ‘dip’ in the middle segment’s elastic modulus occurring around 12 mmHg. The elastic modulus depends on pressure, meaning that unfiltered noise within the filtered pressure interval may have interfered with the modulus calculation. If this dip were accurate, it would indicate that the middle segment of the urethra lost most of its stiffness at 12 mmHg. Though this may be true to some degree, it doesn’t align with the rest of the data. If the harsh noise spikes were to be removed from this plot, both the middle and distal incremental elastic moduli would steadily increase, meaning that each segment increases in stiffness as pressure increases. The stiffness of the material increasing with increasing pressure load makes sense as the urethra is trying to prevent permanent deformation/distension as the circumferential stresses increase.
Circumferential Stress vs. Circumferential Strain
In reference to Figure 5, the circumferential stress-strain relationship is important as it presents how the biological body deforms as a consequence of pressures applied to it. The circumferential stress-strain relationship for the proximal segment followed a nearly identical trend for the stresses and strains at the inner, midwall, and outer radii. As circumferential stress increases so does strain. There is an exponentially direct relationship between the two. When looking back at Figure 2, as internal pressure increases, normalized inner diameter increases thus indicating an increase in strain (deformation) with internal pressure. Consequently, a larger stress is required to resist this deformation. The middle segment plots for all three radii initially exhibiting negative strain then shifting positively can be explained by the negative compliance during the low pressure range. The same reasoning can be used to describe the distal plots for all three radii. In theory, a negative strain indicates compression. In reality, it is known that increasing the pressure inside of a cylinder (approximate shape of the rat urethra) would only create tension, not compression. The hypothesis that was used to explain negative compliance can be used to explain the negative strain: noise in the data.