近年來隨著醫療科技的進步，AI輔助手術及手術模擬等技術快速地發展，故有關生物軟組織之機械行為的研究受到注目，其中手術過程之力與位移的關係對於手術模擬的觸覺及視覺尤其重要，然而生物軟組織表面皆會有組織液等流體之薄膜披覆，在流體能承受負載的情況下，如何得到考慮流體效應之力與位移之數據是很重要的。
本研究使用有限元素法建立一個暫態擠壓軟彈液動潤滑系統，以雷諾方程式耦合超彈性材料模型及負載平衡方程式，探討不同超彈參數、厚度、負載條件下，以剛球擠壓有限厚度之超彈性平板時，其壓力、膜厚、變形量及von Mises應力的變化，並且考慮流體能承受負載，將此模型視為壓痕模擬器，討論流體對力與位移之影響，研究對象則選擇手術過程中需要小負載、且極柔軟之大腦組織的灰質及白質。
由模擬結果得知，若分析之軟材料會產生大變形，由於有限應變理論，應針對模型之假設作修正，線彈性材料模型僅適用於極微小應變，而超彈乾接觸與使用軟彈液動模型之力與位移的差異隨著負載增加而提升。隨著考慮真實厚度於定負載時，變形量隨著厚度增加而增加，但增加的趨勢漸緩。較軟的灰質其變形量大於白質，且隨著厚度增加兩者的變形量差異越大，而在固定變形量時可發現，隨著厚度增加，白質所需要的負載較灰質大。

With the advancement of medical technology, technologies such as AI-assisted surgery and surgical simulation have developed rapidly. The relationship between force and displacement of the surgical procedure is especially important for the tactile and visual aspects of surgical applications. In this study, FEM is used to establish a transient squeeze soft-EHL system. The Reynolds equation coupled hyperelastic material model and the load balance equation were used to investigate different hyperelastic parameters, thickness and load conditions, by giving a constant load to a rigid ball which squeezes finite thickness of the hyperelastic flats. Considering the fluid can withstand the load, using this model as an indentation simulator, discuss the effect of fluid on force and displacement. The gray matter and white matter of brain tissue which is extremely soft and requires a small load during surgery are selected as our studying objects.
The simulation results reveal that the assumptions of the EHL model should be corrected if soft material produced large deformation. The difference between the force and the displacement of the dry contact of hyperelastic model and soft-EHL increases as the load increases. The softer gray matter has a larger deformation than the white matter, and the difference in deformation between the two increases with thickness. When the amount of deformation is fixed, it can be found that as the thickness increases, the load required for the white matter is larger than that of the gray matter.

[1] S. Misra, K. Ramesh, A. M. J. P. T. Okamura, and V. Environments, "Modeling of tool-tissue interactions for computer-based surgical simulation: a literature review," vol. 17, no. 5, pp. 463-491, 2008.
[2] G. Székely et al., "Virtual Reality-Based Simulation of Endoscopic Surgery," vol. 9, no. 3, pp. 310-333, 2000.
[3] L. G. Griffith and G. J. s. Naughton, "Tissue engineering--current challenges and expanding opportunities," vol. 295, no. 5557, pp. 1009-1014, 2002.
[4] M. J. J. o. a. p. Mooney, "A theory of large elastic deformation," vol. 11, no. 9, pp. 582-592, 1940.
[5] R. J. P. T. o. t. R. S. o. L. S. A. Rivlin, Mathematical and P. Sciences, "Large elastic deformations of isotropic materials IV. Further developments of the general theory," vol. 241, no. 835, pp. 379-397, 1948.
[6] P. J. Blatz and W. L. J. T. o. t. S. o. R. Ko, "Application of finite elastic theory to the deformation of rubbery materials," vol. 6, no. 1, pp. 223-252, 1962.
[7] R. W. J. P. o. t. R. S. o. L. A. M. Ogden and P. Sciences, "Large deformation isotropic elasticity–on the correlation of theory and experiment for incompressible rubberlike solids," vol. 326, no. 1567, pp. 565-584, 1972.
[8] O. H. J. R. C. Yeoh and technology, "Some forms of the strain energy function for rubber," vol. 66, no. 5, pp. 754-771, 1993.
[9] Y. J. A. J. o. P.-L. C. Fung, "Elasticity of soft tissues in simple elongation," vol. 213, no. 6, pp. 1532-1544, 1967.
[10] D. Veronda and R. J. J. o. b. Westmann, "Mechanical characterization of skin—finite deformations," vol. 3, no. 1, pp. 111-124, 1970.
[11] C. Wex, S. Arndt, A. Stoll, C. Bruns, and Y. J. B. E. B. T. Kupriyanova, "Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review," vol. 60, no. 6, pp. 577-592, 2015.
[12] L. E. Bilston, "Brain tissue mechanical properties," in Biomechanics of the brain: Springer, pp. 69-89, 2011.
[13] J. Weickenmeier, M. Kurt, E. Ozkaya, M. Wintermark, K. B. Pauly, and E. Kuhl, "Magnetic resonance elastography of the brain: A comparison between pigs and humans," Journal of the Mechanical Behavior of Biomedical Materials, vol. 77, pp. 702-710, 2018/01/01/ 2018.
[14] S. Budday et al., "Mechanical properties of gray and white matter brain tissue by indentation," vol. 46, pp. 318-330, 2015.
[15] J. Van Dommelen, T. Van der Sande, M. Hrapko, and G. J. J. o. t. m. b. o. b. m. Peters, "Mechanical properties of brain tissue by indentation: interregional variation," vol. 3, no. 2, pp. 158-166, 2010.
[16] T. Kaster, I. Sack, and A. J. J. o. b. Samani, "Measurement of the hyperelastic properties of ex vivo brain tissue slices," vol. 44, no. 6, pp. 1158-1163, 2011.
[17] D. Dowson and G. R. Higginson, Elasto-hydrodynamic lubrication: international series on materials science and technology. Elsevier, 2014.
[18] B. J. Hamrock, S. R. Schmid, and B. O. Jacobson, Fundamentals of fluid film lubrication. CRC press, 2004.
[19] Q.-D. Chen and W.-L. Li, "Analysis of Soft-Elastohydrodynamic Lubrication Line Contacts on Finite Thickness," Journal of Tribology, vol. 140, no. 4, p. 041502, 2018.
[20] H. Christensen, "Elastohydrodynamic Theory of Spherical Bodies in Normal Approach," Journal of Lubrication Technology, vol. 92, no. 1, pp. 145-153, 1970.
[21] P. Yang and S. Wen, "Pure squeeze action in an isothermal elastohydrodynamically lubricated spherical conjunction part 1. Theory and dynamic load results," Wear, vol. 142, no. 1, pp. 1-16, 1991/02/01/ 1991.
[22] P. Yang and S. Wen, "Pure squeeze action in an isothermal elastohydrodynamically lubricated spherical conjunction part 2. Constant speed and constant load results," Wear, vol. 142, no. 1, pp. 17-30, 1991/02/01/ 1991.
[23] H. Chu, R. Lee, and Y. Chiou, "Study on pure squeeze elastohydrodynamic lubrication motion using optical interferometry and the inverse approach," Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 218, no. 6, pp. 503-512, 2004.
[24] H.-M. Chu, W.-L. Li, and M.-D. Chen, "Elastohydrodynamic lubrication of circular contacts at pure squeeze motion with non-Newtonian lubricants," Tribology International, vol. 39, no. 9, pp. 897-905, 2006/09/01/ 2006.
[25] L. M. Chu, J.-R. Lin, Y.-P. Chang, and C.-C. Wu, "Elastohydrodynamic lubrication of circular contacts at pure squeeze motion with micropolar lubricants," Industrial Lubrication and Tribology, vol. 68, no. 6, pp. 640-646, 2016.
[26] H. Hertz, "On the contact of elastic solids," Z. Reine Angew. Mathematik, vol. 92, pp. 156-171, 1881.
[27] C. Roelands, J. Vlugter, and H. J. J. o. B. E. Waterman, "The viscosity-temperature-pressure relationship of lubricating oils and its correlation with chemical constitution," vol. 85, no. 4, pp. 601-607, 1963.
[28] D. Dowson and G. R. Higginson, Elasto-hydrodynamic Lubrication: The Fundamentals of Roller and Gear Lubrication. Pergamon Press, 1965.
[29] H. Hencky, "Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen," ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol. 4, no. 4, pp. 323-334, 1924.
[30] J. J. O'Hagan and A. Samani, "Measurement of the hyperelastic properties of tissue slices with tumour inclusion," Physics in Medicine & Biology, vol. 53, no. 24, p. 7087, 2008.
[31] V. Libertiaux, F. Pascon, and S. Cescotto, "Experimental verification of brain tissue incompressibility using digital image correlation," Journal of the Mechanical Behavior of Biomedical Materials, vol. 4, no. 7, pp. 1177-1185, 2011/10/01/ 2011.
[32] M. L. J. Scott, P. A. Bromiley, N. A. Thacker, C. E. Hutchinson, and A. Jackson, "A fast, model-independent method for cerebral cortical thickness estimation using MRI," Medical Image Analysis, vol. 13, no. 2, pp. 269-285, 2009/04/01/ 2009.