Improved Mechanical Characterization of Soft Tissues Including Mounting Stretches
Abstract
:1. Introduction
2. Materials and Methods
2.1. Continuum Mechanics Framework
2.2. Material Parameter Identification Procedures
2.2.1. Standard Fitting Methods
2.2.2. Fitting Including Prestretch Method
2.3. Virtual Biaxial Experiments
2.4. Biaxial Experimental Testing of Human Aortas
3. Results
3.1. Comparison of Fitting Methods and Verification of Fitting with Prestretch Method
3.2. Fitting Including Prestretch Method—Comparison with ‘Linden Method’
3.3. Fitting Data from Biaxial Experiments
4. Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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MP Set | [kPa] | [kPa] | [-] | [°] | [-] |
---|---|---|---|---|---|
Smoljkić M55 | 59.7 | 36.3 | 11.38 | 58.9 | 0.243 |
Weisbecker—media | 14.0 | 140 | 11.90 | 38.4 | 0.210 |
Specimen | Gender | Age | Atherosclerosis Level | Thickness [mm] | Experimental Stretches [-] |
---|---|---|---|---|---|
Donor 1 | Male | 56 | Medium | 1.93 | 1.15 |
Donor 2 | Male | 69 | High | 1.35 | 1.15 |
Donor 2– intima | Male | 69 | - | 0.27 | 1.05 |
Donor 2– media | Male | 69 | - | 0.88 | 1.20 |
Donor 2– adventitia | Male | 69 | - | 0.54 | 1.15 |
Fitting Method | [kPa] | [kPa] | [-] | [°] | [-] | MAE [10−3] | ||
---|---|---|---|---|---|---|---|---|
Standard fitting | 1.005 | 64.9 | 2.47 | 8.12 | 56.9 | 0 | 467.9 | 0.993 |
1.010 | 69.3 | 1.62 | 16.3 | 90.0 | 0.1 | 533.0 | 0.970 | |
1.015 | 71.9 | 2.6 | 1.23 | 90.0 | 0 | 710.5 | 0.879 | |
1.020 | 74.6 | 2.89 | 0 | 90.0 | 0 | 739.6 | 0.868 | |
Standard fitting w. subtraction | 1.005 | 58.7 | 39.9 | 12.06 | 59.0 | 0.246 | 37.9 | 0.999 |
1.010 | 57.7 | 43.7 | 12.77 | 59.1 | 0.248 | 76.7 | 0.998 | |
1.015 | 56.7 | 47.7 | 13.54 | 59.2 | 0.250 | 117.6 | 0.997 | |
1.020 | 55.8 | 51.9 | 14.36 | 59.3 | 0.251 | 159.3 | 0.995 | |
Fitting inc. prestretch | Any value | 59.7 | 36.3 | 11.38 | 58.9 | 0.243 | 0 | 1 |
Ground-truth | 59.7 | 36.3 | 11.38 | 58.9 | 0.243 | - | - |
Fitting Method | [kPa] | [kPa] | [-] | [°] | [-] | MAE [10−3] | R2 | |
---|---|---|---|---|---|---|---|---|
Standard fitting | 1.005 | 10.3 | 43.9 | 4.93 | 41.45 | 0 | 523.2 | 0.981 |
1.010 | 14.3 | 41.1 | 5.57 | 41.16 | 0 | 466.3 | 0.916 | |
1.015 | 18.4 | 38.3 | 6.30 | 40.84 | 0 | 515.0 | 0.781 | |
1.020 | 22.7 | 35.6 | 7.12 | 40.48 | 0 | 564.6 | 0.537 | |
Standard fitting w. subtraction | 1.005 | 14.0 | 147.9 | 12.49 | 38.47 | 0.209 | 22.5 | 0.987 |
1.010 | 14.6 | 157.6 | 13.21 | 38.49 | 0.209 | 57.2 | 0.932 | |
1.015 | 14.2 | 169.4 | 14.07 | 38.48 | 0.211 | 82.7 | 0.852 | |
1.020 | 14.4 | 183.7 | 15.11 | 38.41 | 0.214 | 125.9 | 0.701 | |
Fitting inc. prestretch | Any value | 14.0 | 140 | 11.90 | 38.4 | 0.210 | 0 | 1 |
Ground-truth | 14.0 | 140 | 11.90 | 38.4 | 0.210 | - | - |
Specimen | Method | C1 [kPa] | k1 [kPa] | k2 [-] | α [◦] | κ [-] | [-] | [-] |
---|---|---|---|---|---|---|---|---|
1 | Linden | 5.1 | 20.2 | 2.110 | 89.98 | 0.263 | 1.077 | 1.058 |
FIP | 5.1 | 20.1 | 2.154 | 85.76 | 0.263 | 1.077 | 1.059 | |
2 | Linden | 8.0 | 43.5 | 1.057 | 90.00 | 0.295 | 1.063 | 1.042 |
FIP | 8.0 | 44.0 | 1.138 | 90.00 | 0.298 | 1.060 | 1.044 | |
3 | Linden | 1.0 | 18.6 | 0.029 | 46.86 | 0.059 | 1.066 | 1.043 |
FIP | 2.4 | 21.3 | 0.039 | 46.60 | 0.120 | 1.056 | 1.052 | |
4 | Linden | 6.8 | 41.0 | 0.322 | 90.00 | 0.277 | 1.074 | 1.037 |
FIP | 6.7 | 41.7 | 0.281 | 90.00 | 0.279 | 1.075 | 1.039 | |
5 | Linden | 4.4 | 19.9 | 0.538 | 54.39 | 0.096 | 1.092 | 1.027 |
FIP | 3.8 | 18.8 | 0.475 | 54.00 | 0.067 | 1.104 | 1.021 |
Specimen | Method | C1 [kPa] | k1 [kPa] | k2 [-] | α [◦] | κ [-] | [-] | [-] | |
---|---|---|---|---|---|---|---|---|---|
Donor 1 | SF | 14.51 | 4.255 | 127.87 | 90.00 | 0.210 | - | - | <0 |
SFS | 11.55 | 0.768 | 39.07 | 61.00 | 0 | - | - | <0 | |
FIP | 12.21 | 0.37 | 31.35 | 60.88 | 0 | 1.003 | 1.028 | 0.99 | |
Donor 2 | SF | 30.53 | 57.85 | 171.20 | 90.00 | 0.239 | - | - | <0 |
SFS | 24.90 | 65.80 | 174.57 | 90.00 | 0.243 | - | - | <0 | |
FIP | 25.87 | 39.78 | 139.88 | 90.00 | 0.241 | 1.009 | 1.016 | 0.99 | |
Donor 2—intima | SF | 3.78 | 4.68 | 76.73 | 90.00 | 0.003 | <0 | ||
SFS | 2.13 | 39.65 | 374.63 | 90.00 | 0.221 | 0.87 | |||
FIP | 2.14 | 26.88 | 268.30 | 90.00 | 0.206 | 1.017 | 1.004 | 0.99 | |
Donor 2—media | SF | 5.28 | 10.21 | 2.57 | 37.74 | 0 | 0.96 | ||
SFS | 2.78 | 13.35 | 2.06 | 39.26 | 0 | 0.98 | |||
FIP | 2.98 | 12.47 | 1.88 | 39.00 | 0 | 1.009 | 1.010 | 0.99 | |
Donor 2—adventitia | SF | 2.70 | 0.41 | 31.04 | 52.40 | 0 | <0 | ||
SFS | 1.99 | 0.62 | 27.77 | 51.32 | 0 | <0 | |||
FIP | 2.10 | 0.41 | 23.85 | 51.21 | 0 | 1.009 | 1.019 | 0.99 |
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Škugor, T.; Virag, L.; Sommer, G.; Karšaj, I. Improved Mechanical Characterization of Soft Tissues Including Mounting Stretches. Math. Comput. Appl. 2024, 29, 55. https://doi.org/10.3390/mca29040055
Škugor T, Virag L, Sommer G, Karšaj I. Improved Mechanical Characterization of Soft Tissues Including Mounting Stretches. Mathematical and Computational Applications. 2024; 29(4):55. https://doi.org/10.3390/mca29040055
Chicago/Turabian StyleŠkugor, Toni, Lana Virag, Gerhard Sommer, and Igor Karšaj. 2024. "Improved Mechanical Characterization of Soft Tissues Including Mounting Stretches" Mathematical and Computational Applications 29, no. 4: 55. https://doi.org/10.3390/mca29040055