## 7 Conclusions  
Analysis of the results from the numerical analyses performed for spherical, flat, and rounded indenters allows us to conclude that there are no significant differences in the results obtained that could be related to the mathematical model used. For the adopted rheological models of Oghen and Yeoh, comparable results were obtained. Their differences oscillate at the level of 5%, which can be considered a very good fit. A greater divergence of results is observed in the parameters of material constants used for numerical calculations. The differences obtained when changing the constants oscillate within \(\pm\) 32%, which may indicate a satisfactory fit. This may be due to the large discrepancy in the initial data of the rheological models. Measurement of the stiffness and attenuation of the ultrasound wave with the FibroScan(r) device carried out on the CIRS Model 039 phantoms allows us to conclude that the average measured values do not deviate from the manufacturer's stated values. It was found that as the stiffness of the phantom increases, the scatter of the results increases. For all phantoms tested with attachments, attenuation values less than the limit value of 300 dB/m were recorded. The results obtained allowed the thesis that the thickness of the selected materials (Agar Progel, Medical Gel #0, Ecoflex 00-20) should be as small as possible so that the unfavorable value of wave attenuation does not occur. The attenuation of ultrasound in the skin increases with frequency and averages a few to several dB/cm in the frequency range of 1.0-5.0 MHz. Too much attenuation in the attachment can weaken the ultrasound wave entering the liver tissue and introduce measurement errors or make measurements impossible. Durable gel- or rubber-like materials with ultrasound attenuation in the range of a few to several dB/cm are available. The use of the Johnson-Cook elastic-plastic rheological model to describe bone tissue shows a very good fit for both the compact and spongy parts. At the same time, using the hybrid FEM/SPH method in this case shows a very good fit. The spongy structure of the bone is ideal for modeling with the SPH method. During the phenomenon of wave passage through the ribs, a wave front is observed, propagating first along the area of higher stiffness, in this case the cortical structure of the bone. Then, a weaker wavefront is seen in the spongy substance. It is concluded that there is a directly proportional relationship between stiffness and the speed of wave propagation. The higher the stiffness, and thus the higher the value of Young's modulus, the higher the speed of wave propagation in the object. In addition, absorption of the forced wave in the spongy part of the bone is observed. The presented results of the numerical analysis of the preliminary check of the efficiency in the propagation of a mechanical wave due to the application of the measuring part of the FibroScan(r) elastograph to the examined organ demonstrate the correctness of the assumed methodology. The result of the wave speed (1569 m/s) correlates with the value for a healthy liver (1550 m/s), which is a very good match. Data curation, K.K. ; Formal analysis, K.R. and R.S. ; Investigation, K.R. and K.O. ; Methodology, D.P. and K.O. ; Project administration, D.P. and R.S. ; Resources, K.R. and R.S. ; Supervision, K.J. and K.O. ; Validation, D.P. and K.O. ; Writing--original draft, K.K. and K.J. ; Writing--review & editing, D.P., K.K. and K.J. All authors have read and agreed to the published version of the manuscript. Not applicable. Data Availability Statement: Data sharing is not applicable to this article. The data are owned by TIBA Ltd., and not publicly available. Calculations have been carried out in Wroclaw Centre for Networking and Supercomputing ([[http://www.wcss.pl](http://www.wcss.pl)]([http://www.wcss.pl](http://www.wcss.pl))), grant No. 452. [PERSON] is co-owner of TIBA Ltd. and also co-author of the article.