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Mechanical Properties of Mouse Lung Cells and Their Effects on the Atomic Force Microscope Beam Vibrations

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Abstract

In the present investigation, the mechanical properties of mouse normal and carcinomatous (LL/2) lung tissue cells were investigated using atomic force microscopy (AFM). The normal lung cells have been derived directly from C57BL mice. Initially, the elastic modulus of LL/2 cells was measured following chemotherapy with the anti-cancer drug Cisplatin and plasma treatment. MTT evaluation was used to determine the optimal dosages for 24- and 48-h incubations based on the IC50 cell viability concentration during chemotherapy treatment. After 24 and 48 h, the results demonstrated that Cisplatin-based chemotherapy increases the elastic modulus of LL/2 cells by 1.599 and 2.308 times compared to untreated cells. LL/2 cells were subsequently treated with plasma for 30 and 60 s for 24 and 48-h incubation. The plasma treatment decreased the LL/2 cell’s elastic modulus, and the time duration of plasma treatment increased the reduction amount of elastic modulus. During the second section of the study, theoretical (finite element analysis [FEM]) and experimental techniques were used to examine the resonant frequencies and magnitude of the frequency response function (FRF) of the AFM cantilever’s movements when applying normal and cancerous cells before and after chemo and plasma treatments as specimens. The results indicated that increasing the samples’ elastic modulus raises the resonant frequency, so the resonant frequency of treated cells as a sample is greater than untreated cells. In conclusion, the FEM and experimental results were compared and found to be in good agreement.

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No datasets were generated or analyzed during the current study.

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Authors and Affiliations

  1. Biomedical Department, Central Tehran Branch, Islamic Azad University, Damavand, Iran

    Nazanin Maleki Zadeh

  2. Renewable Energy Research Center, Damavand Branch, Islamic Azad University, Damavand, Iran

    Ali Sadeghi & Mansoureh Lafouti

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  1. Nazanin Maleki Zadeh
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  2. Ali Sadeghi
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  3. Mansoureh Lafouti
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Contributions

N. Maleki Zadeh prepared the figures and tablas, A. Sadeghi write the paper and M. Lafouti worked on programming and software works. All authors reviewed the manuscript.

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Correspondence to Ali Sadeghi.

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Appendix A. Timoshenko Cantilever Inertia and Stiffness Matrices

Appendix A. Timoshenko Cantilever Inertia and Stiffness Matrices

The elements of inertia, stiffness have been written due to Timoshenko cantilever law as [52]:

$${[k]}_{e}=\frac{12}{({L}^{2}+12g)}\frac{EI}{L}\left[\begin{array}{cccc}1 & & & Sym\\ \frac{L}{2} & \frac{{L}^{2}}{3}+g & & \\ -1 & -\frac{L}{2} & 1 & \\ \frac{L}{2} & \frac{{L}^{2}}{6}-g & -\frac{L}{2} & \frac{{L}^{2}}{3}+g\end{array}\right]$$
(A1)
$${[m]}_{e}={[{m}_{t}]}_{e}+{[{m}_{r}]}_{e}$$
(A2)

\({[{m}_{t}]}_{e}\) and \({[{m}_{r}]}_{e}\) introduce the inertia matrix for shear inertia and rotatory inertia influences respectively.

$${[{m}_{t}]}_{e}=\frac{\rho AL}{{({L}^{2}+12g)}^{2}}\left[\begin{array}{cccc}{t}_{11} & & & Sym\\ {t}_{21} & {t}_{22} & & \\ {t}_{31} & {t}_{32} & {t}_{33} & \\ {t}_{41} & {t}_{42} & {t}_{43} & {t}_{44}\end{array}\right]$$
(A3)
$$\begin{array}{ll}{t}_{11}=(\frac{13}{35}{L}^{4}+\frac{42}{5}g{L}^{2}+48{g}^{2}),\,{t}_{21}=(\frac{11}{210}{L}^{4}+\frac{11}{10}g{L}^{2}+6{g}^{2})L,\\ {t}_{31}=(\frac{9}{7}{L}^{4}+\frac{18}{5}g{L}^{2}+24{g}^{2}),\,{t}_{32}=(\frac{13}{420}{L}^{4}+\frac{9}{10}g{L}^{2}+6{g}^{2})L,\\ {t}_{22}=(\frac{1}{105}{L}^{4}+\frac{1}{5}g{L}^{2}+\frac{6}{5}{g}^{2}){L}^{2},\,{t}_{42}=-(\frac{1}{140}{L}^{4}+\frac{1}{5}g{L}^{2}+\frac{6}{5}{g}^{2}){L}^{2},\\ {t}_{33}={t}_{11},\,{t}_{41}=-{t}_{32},\,{t}_{43}=-{t}_{21},\,{t}_{44}={t}_{22}\end{array}$$
(A4)
$${[{m}_{r}]}_{e}=\frac{\rho AL}{{({L}^{2}+12g)}^{2}}{\left(\frac{r}{L}\right)}^{2}\left[\begin{array}{cccc}{r}_{11} & & & Sym\\ {r}_{21} & {r}_{22} & & \\ {r}_{31} & {r}_{32} & {r}_{33} & \\ {r}_{41} & {r}_{42} & {r}_{43} & {r}_{44}\end{array}\right]$$
(A5)
$$\begin{array}{ll}{r}_{11}=\frac{6}{5}{L}^{4},\,{r}_{21}=(\frac{1}{10}{L}^{2}-6{g}^{2}){L}^{3},\,{r}_{22}=(\frac{2}{15}{L}^{4}+2g{L}^{2}+48{g}^{2}){L}^{2},\,{r}_{31}=-{r}_{11},\,{r}_{32}=-{r}_{21},\\ \,{r}_{33}={r}_{11},\,{r}_{41}={r}_{21},\,{r}_{43}=-{r}_{21},\,{r}_{44}={r}_{22},\,{r}_{42}=(\frac{-1}{30}{L}^{4}-2g{L}^{2}+24{g}^{2}){L}^{2}\end{array}$$
(A6)
$$g=\frac{EI}{kGA}\,and\,r=\sqrt{\frac{I}{A}}$$

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Zadeh, N.M., Sadeghi, A. & Lafouti, M. Mechanical Properties of Mouse Lung Cells and Their Effects on the Atomic Force Microscope Beam Vibrations. Cell Biochem Biophys (2024). https://doi.org/10.1007/s12013-024-01259-z

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