PSI - Issue 65

Galina Eremina et al. / Procedia Structural Integrity 65 (2024) 92–96 Galina Eremina, Alexey Smolin/ Structural Integrity Procedia 00 (2024) 000–000

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stopping the growth of primary and secondary cancer tumours in bone tissues from 40 kPa to 0.15 MPa. Thus, mechanical action can also play a key role in stimulating the activity of both tumour and bone cells and can play a key role in antitumour therapy Mpekris et al. (2023). At the same time, large values of external mechanical impact can lead to degradation of bone tissue. Therefore, it is relevant to study the effect of the level of mechanical stimulation (SWT) on bone tissue affected by neoplastic processes in order to regenerate bone tissue and deactivate cancerous cells. In connection with the above, the purpose of this work is to develop a numerical model of the mechanical behavior of osteosarcoma under shock wave loading.

2. Calculation

2.1. Movable cellular automaton method for poroelastic body

The need to vary the characteristic loading rates over a wide range and the need to take into account the destruction of solid-phase components determined the choice of computer modeling using the particles-based method as the main research method. Representatives of the particle method used to solve the problem are the movable cellular automata (MCA) method and the hybrid cellular automata (HCA, for research at higher scale levels taking into account biological fluids). The movable cellular automata method is an effective discrete method for modeling the mechanics of heterogeneous materials at various scales. It has been established that discrete methods have proven themselves well for modeling the mechanical behavior of biomaterials and metals under dynamic loading at the micro- and mesolevels is shown by Eremina et al. (2021). In the MCA, the modeled material is considered as an ensemble of discrete elements (cellular automata) interacting with each other according to certain rules, which makes it possible to describe its deformation behavior as an isotropic elastic-plastic body within the framework of the discrete approach. The motion of the ensemble of elements is described by the Newton-Euler equations. The main advantage of the method for solving the stated problems is the ability to explicitly take account of the structure and discontinuities of the material and modeling failure is shown by Smolin et al. (2014). The basis of the HCA method is the decomposition of the problem being solved into two subproblems: 1) description of the mechanical behavior of the enclosing solid body (framework) and 2) description of fluid transfer in the filtration volume, represented by a system of interconnected channels, pores, cracks, etc. The MCA method is used to describe the mechanical behavior of the enclosing body. The influence of the fluid contained in the crack-pore space of the cellular automaton on its stress-strain state is described based on the linear Biot poroelasticity model Smolin et al. (2021).

Table 1. Poroelastic parameters of tumor and cancellous tissue.

Porosity  Permeability, m 2 Compression strength, σ MPa

Bone tissue Bulk modulus of the solid phase, K s , GPa

Bulk modulus of the matrix, K , GPa

Shear modulus of the matrix, G , GPa

Density of the matrix, ρ kg/m 3

1.010 18 1.010 16

Tumor

10.0

0.000101

0.0000203

700 800

0.70 0.80

-

Cancellous 17.0

3.3

1.32

10

The poroelastic parameters are presented in Table 1. The fluid in both bone tissues is assumed to be the same and equivalent to salt water, with a bulk modulus K f = 2.4 GPa, and density ρ f = 1000 kg/m 3 . The creation of conditions for the processes of tumour destruction, formation of protective stroma, regeneration of bone tissue in the affected areas will be assessed by such criteria as the magnitude of hydrostatic pressure, fluid pressure in pores and deformation intensity. We consider it appropriate to introduce models of biological tissue restructuring (such as Wolf's law) only when considering static loads, when the magnitude of the impact is constant over time. Within the framework of this study, it is assumed that the shock wave effect is short-term (<30 minutes per day), the rest of the time the patient can exhibit high physical activity accompanied by a change in physiological position and intensity of physical activity. The construction of models for such complex behaviour is currently not possible worldwide due to the limitation of computing resources and data for model validation.