# Mechanically Induced Cavitation in Biological Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background: Static and Dynamic Approaches

#### 2.1. Static Approach

^{T}, where F is the deformation gradient tensor [42]), i and j are free indices, and k is a dummy index.

#### 2.2. Dynamics

## 3. Experimental Methods for Cavitation-Induced Damage to the Biological Systems

#### 3.1. Needle-Induced Cavitation

^{−1}–10

^{−3}s

^{−1}). Zimberlin et al. [31] first demonstrated the use of NIC for in vivo samples [84] by measuring the elastic modulus of the bovine eye (more specifically, the vitreous body in an eye (shown in Figure 2) [84,85]. Similarly, it has been reported that biological organs have location-dependent elastic moduli (e.g., the elastic moduli measured in the areas of the nucleus and cortex parts in an extracted bovine eye (see Figure 2) were 11.8 and 0.8 kPa, respectively [85]).

^{−1}–10

^{−3}s

^{−1}).

#### 3.2. Acoustically Induced Cavitation

^{3}to 10

^{8}s

^{−1}. Using this new method, the mechanical properties of agarose hydrogel were quantified [87].

#### 3.3. Laser-Induced Cavitation

^{1}–10

^{8}) with an emphasis on underlying injury mechanisms in the human body including for traumatic brain injuries [27]. Because the LIC is based on the focused laser beam, it can be used to probe the dynamics of cavitation bubbles at different locations within a sample. This is an attractive feature for characterizing localized material properties of soft gels. For example, experimentally measured bubble dynamics over time have been analyzed and compared with theoretical analysis to predict material properties at 10

^{3}–10

^{8}strain rates [27]. Brujan et al. investigated the interaction of a single bubble with hydrogel and showed the relationship between the elastic modulus and bubble dynamics such as jetting behavior, jet velocity, bubble oscillation time, bubble migration, and bubble erosion. For example, polyacrylamide gel with 0.25 MPa elastic modulus has a maximum liquid jet velocity of 960 ms

^{−1}, which can infiltrate the elastic boundary thickness [127]. This jetting ejection and the tensile stress from the bubble collapse can influence the ablation process during short-pulsed laser surgery.

#### 3.4. Integrated Drop Tower System

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Cell membrane damage in the presence of a microbubble oscillated by ultrasound. (

**a**) Damage and repair of bovine endothelial monolayer cells measured over time in propidium iodide (PI) and Fura 2 fluorescence [111]. (

**b**) Time-lapse results of PI (B,E) and Calcium (C,F) changes in bEnd.3 cells with (A,B,C) or without shear stress (D,E,F) [112].

**Figure 4.**(

**a**–

**c**) Procedure of seeded laser-induced cavitation (SLIC) from cavitation nucleation to collapse. Magnified image of eicosane flakes around an ablation seed (

**d**) before and (

**e**) after SLIC. (

**f**) Maximum cavity size with respect to seed diameter and laser-pulse energy [81].

**Figure 5.**Characterization of cell injury depending on drop height using Hs27 fibroblasts (x-axis: time and y-axis: average confluency). (

**a**) The average confluency graph for 30 and 40 cm drops. (

**b**) The local confluency graph for 40 cm drop. (

**c**,

**d**) Live cell images during 40 cm drop (

**c**) before and (

**d**) after impact [146].

**Table 1.**The equation of elastic stress tensor and constitutive strain functions with different types of models with relevant material parameter.

Name of Model | Strain Energy Density (W) | Reference |
---|---|---|

Neo-Hookean Model | $\frac{\mu}{2}\left({I}_{1}-3\right)$ | [43] |

Mooney–Rivlin Model | $\frac{\mu}{2}\left[c\left({I}_{1}-3\right)+\left(1-c\right)\left({I}_{2}-3\right)\right]$ | [44,45] |

Gent Model | $\frac{\mu}{2}{I}_{m}\mathrm{ln}\left(\frac{{I}_{m}}{{I}_{m}-{I}_{1}+3}\right)$ | [47] |

Ogden Model | $\frac{2\mu}{{N}^{2}}\left({\lambda}_{r}^{N}+{\lambda}_{\theta}^{N}+{\lambda}_{\varphi}^{N}-3\right)$ | [49] |

Fung Model | $\frac{\mu}{2\alpha}{e}^{\alpha \left({I}_{1}-3\right)}$ | [52,53] |

**Table 2.**Summary of linear constitutive models [66].

Name of Model | Strain Energy Density (W) | Description | Reference |
---|---|---|---|

Newtonian | ${\sigma}_{rr}=2\nu {\dot{\epsilon}}_{rr}$ | Viscous stresses linearly dependent on the local strain rate | [67] |

Kelvin–Voigt | ${\sigma}_{rr}=2\left(\mu {\epsilon}_{rr}+\nu {\dot{\epsilon}}_{rr}\right)$ | A spring and a dashpot in parallel; Viscoelastic solid; Creep behavior | [41,68,69] |

Maxwell | $2\nu {\dot{\epsilon}}_{rr}=\frac{\nu}{\mu}{\dot{\sigma}}_{rr}+{\sigma}_{rr}$ | A spring and a dashpot in series; Viscoelastic liquid; Stress relaxation | [70,71] |

Standard Linear solid | $\frac{v}{\mu}{\dot{\sigma}}_{rr}+{\sigma}_{rr}=2\mu {\epsilon}_{rr}+2\nu {\dot{\epsilon}}_{rr}$ | Both creep and stress relaxation | [72] |

NIC | AIC | LIC | Drop Tower Test | |
---|---|---|---|---|

Driving force | Pressure energy | Wave energy | Potential energy | |

Strain rate | 10^{−4}–10^{3} | 10^{3}–10^{8} | 10^{1}–10^{8} | 10^{0}–10^{5} |

Scale (µm) | 10^{0}–10^{5} | 10^{3} | 10^{−1}–10^{2} | 10^{2}–10^{5} |

Pressure (Pa) | ≤10^{5} | ≤10^{7} | ≤10^{8} | ≤10^{6} |

Cavity type | Single | Multiple | Single and Multiple | Single and Multiple |

Level of accessibility | Low | High | High | Intermediate |

Approach type | Contact | Noncontact | Noncontact | Noncontact |

Thermal effect | Low | Intermediate | High | Low |

Application | Drug delivery | Lithotripsy Imaging, Drug delivery | Drug delivery, Microsurgery, Medical diagnostic, High strain rate material properties | High strain rate material properties (Isothermal) |

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Kim, C.; Choi, W.J.; Ng, Y.; Kang, W.
Mechanically Induced Cavitation in Biological Systems. *Life* **2021**, *11*, 546.
https://doi.org/10.3390/life11060546

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Kim C, Choi WJ, Ng Y, Kang W.
Mechanically Induced Cavitation in Biological Systems. *Life*. 2021; 11(6):546.
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Kim, Chunghwan, Won June Choi, Yisha Ng, and Wonmo Kang.
2021. "Mechanically Induced Cavitation in Biological Systems" *Life* 11, no. 6: 546.
https://doi.org/10.3390/life11060546