Undergraduate University of California, San Diego Ladera Ranch, California, United States
Introduction:: Cardiovascular disease is the leading cause of death in the United States.¹ Researchers attempt to model the heart in an effort to understand these disorders, but it proves difficult considering the heart’s complex composition. Planar biaxial testing was first developed by Y.C. Fung in the mid twentieth century, and it was applied on soft tissues in order to derive the mechanical properties of specific biological samples.⁴ In recent years, planar biaxial testing has grown in prevalence in order to properly model physiological developments and their impact on the characteristics of soft tissues. There is a particular interest in modeling for cardiovascular biomechanics and how it corresponds to physiological disorders. Measuring the stress on the heart is of particular interest, but is difficult since stress is not a definite unit of measurement. However, stress can be derived using constitutive equations relating stress and strain. In a study conducted by Velez-Rendon, planar biaxial testing is applied to right ventricular samples in order to model the characteristics of the tissue before and after the propagation of pulmonary arterial hypertension. ⁴ In this paper, a similar planar biaxial experiment is repeated to derive unique data and properties of right ventricular myocardium, and it will be utilized to measure strain. Derived constitutive equations for the myocardium sample will help measure the stress that cannot be directly measured and provide insight for the loads which the heart can sustain.
Materials and Methods:: Prior to the mechanical testing of the right ventricular myocardium, a viable sample for the apparatus must first be obtained. The sample is taken from the myocardium of a rat’s right ventricle, and its size was determined based on the heart's overall morphology in finding the largest square on the right ventricle sample that has an overall uniform thickness. The sample has to be large enough where the hooks for biaxial testing can be attached and there is a large enough area for the markers to be placed to analyze for strain. However, the sample with the markers must be able to be in the field of view for the camera for it to record the pixel positions at specific time points.
A Bose Electro Force plan biaxial testing device is used. ⁴ The Bose device mechanically stretches the preloaded biological sample using four hooks attached to each of the four faces of the sample, making a total of sixteen hooks. There is a flexible suture line attached to these hooks to stretch the sample. For stress derivations, there are two load cells, each attached to one of the principal directions, which springs that possess a calibrated gram load to correspond to a certain voltage, and the Bose system converts these voltages to digital information that can be recorded on the computer. This information from the grams and voltage relationship during the testing is used to calculate force which is then applied to the cross sectional area for stress.
Results, Conclusions, and Discussions:: Based on the results of the planar biaxial testing experiment, the right ventricular myocardium sample is concluded to be anisotropic with more stiffness being present in the circumferential axis compared to the apex to outflow axis. While the load was being applied to the sample tissue, the myocardium demonstrated pseudoelastic properties with negligible hysteretic loops for each of the loading and unloading conditions. The deformation gradient tensor describes a change in shape of the biological tissue from a reference configuration to the deformed configuration under planar biaxial testing. The shear components of the deformation gradient tensor are close to zero because there are minimal shear deformations. The normal deformations are indicative of the 10% protocol maximum for deformation. The figures relating the stress-strain relationships for the right ventricular myocardium sample demonstrate that with more trials over time, the sample begins to precondition over time. The hysteresis loops become closer together within the last trials, showing this preconditioning from numerous loading and unloading cycles. The decreasing area between the hysteresis loops also demonstrate dissipated energy as a result of the preconditioning. Furthermore, the sample is observed to be stiffer along the X1 axis compared to the X2 axis. For the X1 axis, the sample is observed to have more stress acting upon it at smaller strains compared to the X2 axis. There is more stiffness in this circumferential axis than the apex to output axis, and such variable stiffness is characteristic of anisotropic tissue. The E11 and E22 strains which were previously calculated have their own relationship which can be analyzed to determine the isotropy of the myocardium sample. To conclude, the results regarding the mechanical properties of the right ventricular myocardium structure validates previous research and supplements the known constitutive relationship between stress and strain in biological tissues. The tissue was found to be anisotropic and possess pseudoelastic properties that match its function in cardiac tissue for the heart to contract normally. This experiment and its results emphasize the importance of deriving the mechanical properties of cardiac structures while also providing data to assist in pursuing future and modeling.
Acknowledgements (Optional): : I would like to thank my mentor and professor Dr. Daniela Valdez-Jasso for her guidance during the experimental process along with graduate student researchers Vaishali Harimani and Jessica Huberts for their insight.
References (Optional): : [1] Centers for Disease Control and Prevention. (2022, October 14). Heart disease facts. Centers for Disease Control and Prevention. Retrieved March 19, 2023, from https://www.cdc.gov/heartdisease/facts.htm#:~:text=Heart%20disease%20is%20the%20leading,groups%20in%20the%20United%20States.&text=One%20person%20dies%20every%2034,United%20States%20from%20cardiovascular%20disease.
[2] Costa, K. D., Holmes, J. W., & Mcculloch, A. D. (2001). Modelling cardiac mechanical properties in three dimensions. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 359(1783), 1233–1250. https://doi.org/10.1098/rsta.2001.0828
[3] Fehervary, H., Smoljkić, M., Vander Sloten, J., & Famaey, N. (2016). Planar biaxial testing of soft biological tissue using rakes: A critical analysis of protocol and fitting process. Journal of the Mechanical Behavior of Biomedical Materials, 61, 135–151. https://doi.org/10.1016/j.jmbbm.2016.01.011
[4]Vélez-Rendón, D., Pursell, E. R., Shieh, J., & Valdez-Jasso, D. (2019). Relative contributions of matrix and myocytes to biaxial mechanics of the right ventricle in pulmonary arterial hypertension. Journal of Biomechanical Engineering, 141(9). https://doi.org/10.1115/1.4044225
[5] Zhang, W., Feng, Y., Lee, C.-H., Billiar, K. L., & Sacks, M. S. (2015). A generalized method for the analysis of planar biaxial mechanical data using tethered testing configurations. Journal of Biomechanical Engineering, 137(6). https://doi.org/10.1115/1.4029266
