Small-on-Large Fractional Derivative–Based Single-Cell Model Incorporating Cytoskeleton Prestretch

AbstractIn recent years, experimental evidences have suggested important direct implications of viscoelasticity of human cells and cell cytoskeleton dynamics on some relevant collective and single-...

[1]  R. Esenaliev,et al.  Effect of 5-fluorouracil, Optison and ultrasound on MCF-7 cell viability. , 2006, Ultrasound in medicine & biology.

[2]  N. Pugno,et al.  An elastomechanical model for tumor invasion , 2006 .

[3]  Nicola Pugno,et al.  A novel model for porous scaffold to match the mechanical anisotropy and the hierarchical structure of bone , 2014 .

[4]  R. Bagley,et al.  A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity , 1983 .

[5]  Mehdi Nikkhah,et al.  The cytoskeletal organization of breast carcinoma and fibroblast cells inside three dimensional (3-D) isotropic silicon microstructures. , 2010, Biomaterials.

[6]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[7]  Nathan J. Sniadecki,et al.  Review on Cell Mechanics: Experimental and Modeling Approaches , 2013 .

[8]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[9]  Massimiliano Fraldi The Mechanical Beauty of Hierarchically Organized Living Structures , 2014 .

[10]  C. Bakal,et al.  The forces of cancer , 2019, Philosophical Transactions of the Royal Society of London. Biological Sciences.

[11]  R. Koeller Applications of Fractional Calculus to the Theory of Viscoelasticity , 1984 .

[12]  Eitan Kimmel,et al.  Low intensity ultrasound perturbs cytoskeleton dynamics. , 2012, Soft matter.

[13]  Matthew J. Paszek,et al.  Balancing forces: architectural control of mechanotransduction , 2011, Nature Reviews Molecular Cell Biology.

[14]  Ph. Moretto,et al.  3D imaging of microscopic structures using a proton beam , 2005, IEEE Transactions on Nuclear Science.

[15]  J. Rao,et al.  Nanomechanical analysis of cells from cancer patients. , 2007, Nature nanotechnology.

[16]  Axel Niendorf,et al.  Passive and active single-cell biomechanics: a new perspective in cancer diagnosis , 2009 .

[17]  M. Di Paola,et al.  A generalized model of elastic foundation based on long-range interactions: Integral and fractional model , 2009 .

[18]  M. Lekka,et al.  Cancer cell recognition--mechanical phenotype. , 2012, Micron.

[19]  W. M. Haynes CRC Handbook of Chemistry and Physics , 1990 .

[20]  L. Beda Thermal physics , 1994 .

[21]  P. G. Nutting,et al.  A new general law of deformation , 1921 .

[22]  R. C. Weast CRC Handbook of Chemistry and Physics , 1973 .

[23]  Stanislav Y Emelianov,et al.  Gas bubble and solid sphere motion in elastic media in response to acoustic radiation force. , 2005, The Journal of the Acoustical Society of America.

[24]  G. W. Scott Blair,et al.  VI. An application of the theory of quasi-properties to the treatment of anomalous strain-stress relations , 1949 .

[25]  Kristina Haase,et al.  Investigating cell mechanics with atomic force microscopy , 2015, Journal of The Royal Society Interface.

[26]  N. Tschoegl The Phenomenological Theory of Linear Viscoelastic Behavior , 1989 .

[27]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[28]  Federico Bosia,et al.  Hierarchical fiber bundle model to investigate the complex architectures of biological materials. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Miguel García-Sánchez A multilevel approach , 2016 .

[30]  S. Suresh,et al.  Cell and molecular mechanics of biological materials , 2003, Nature materials.

[31]  Luca Deseri,et al.  The Concept of a Minimal State in Viscoelasticity: New Free Energies and Applications to PDEs , 2006 .

[32]  Christopher E. Brennen,et al.  A Review of Added Mass and Fluid Inertial Forces , 1982 .

[33]  Qing‐Li Zhao,et al.  Role of intracellular calcium ions and reactive oxygen species in apoptosis induced by ultrasound. , 2004, Ultrasound in medicine & biology.

[34]  R Lemor,et al.  Cell specific ultrasound effects are dose and frequency dependent. , 2013, Annals of anatomy = Anatomischer Anzeiger : official organ of the Anatomische Gesellschaft.

[35]  Julia E. Sero,et al.  The forces of cancer , 2019, Philosophical Transactions of the Royal Society B.

[36]  C. A. Condat,et al.  A multilevel approach to cancer growth modeling. , 2008, Journal of theoretical biology.

[37]  J. Riley,et al.  Equation of motion for a small rigid sphere in a nonuniform flow , 1983 .

[38]  Zbigniew Stachura,et al.  Cancer cell detection in tissue sections using AFM. , 2012, Archives of biochemistry and biophysics.

[39]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[40]  Stevan Pilipović,et al.  A diffusion wave equation with two fractional derivatives of different order , 2007 .

[41]  A. B. Basset,et al.  A treatise on hydrodynamics with numerous examples , 1888 .

[42]  Z. Stachura,et al.  Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy , 1999, European Biophysics Journal.

[43]  F. Mainardi An historical perspective on fractional calculus in linear viscoelasticity , 2010, 1007.2959.

[44]  J. Ellwart,et al.  Cell membrane damage by ultrasound at different cell concentrations. , 1988, Ultrasound in medicine & biology.

[45]  G. Grillo,et al.  On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density , 2014, 1403.5293.

[46]  S. Salzberg,et al.  The response of normal and malignant cells to ultrasound in vitro. , 1993, Ultrasound in medicine & biology.

[47]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[48]  Helmut Schiessel,et al.  Hierarchical analogues to fractional relaxation equations , 1993 .

[49]  E. Kimmel,et al.  Modeling linear vibration of cell nucleus in low intensity ultrasound field. , 2009, Ultrasound in medicine & biology.

[50]  I. Nishio,et al.  Colloidal crystal: bead–spring lattice immersed in viscous media , 2001 .

[51]  M. Davidson,et al.  The cancer glycocalyx mechanically primes integrin-mediated growth and survival , 2014, Nature.

[52]  N. Pugno,et al.  A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells , 2015, Journal of The Royal Society Interface.

[53]  C. Lim,et al.  AFM indentation study of breast cancer cells. , 2008, Biochemical and biophysical research communications.

[54]  L. Deseri,et al.  The state of fractional hereditary materials (FHM) , 2014 .

[55]  Ehsan Gazi,et al.  Measurement of elastic properties of prostate cancer cells using AFM. , 2008, The Analyst.

[56]  S. Cowin,et al.  Inhomogeneous elastostatic problem solutions constructed from stress-associated homogeneous solutions , 2004 .

[57]  Gianpietro Del Piero,et al.  On The Concepts of State and Free Energy in Linear Viscoelasticity , 1997 .

[58]  Manfred Radmacher,et al.  Comparison of mechanical properties of normal and malignant thyroid cells. , 2012, Micron.

[59]  Masoud Agah,et al.  The effects of cancer progression on the viscoelasticity of ovarian cell cytoskeleton structures. , 2012, Nanomedicine : nanotechnology, biology, and medicine.

[60]  Lennart D Johns,et al.  Nonthermal effects of therapeutic ultrasound: the frequency resonance hypothesis. , 2002, Journal of athletic training.

[61]  S. Salzberg,et al.  Distinct sensitivity of normal and malignant cells to ultrasound in vitro. , 1997, Environmental health perspectives.

[62]  M. Radmacher,et al.  Comparison of the viscoelastic properties of cells from different kidney cancer phenotypes measured with atomic force microscopy , 2013, Nanotechnology.

[63]  Nicholas W. Tschoegl,et al.  The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction , 1989 .

[64]  Massimiliano Zingales,et al.  Power‐law hereditariness of hierarchical fractal bones , 2013, International journal for numerical methods in biomedical engineering.

[65]  James K Gimzewski,et al.  AFM-based analysis of human metastatic cancer cells , 2008, Nanotechnology.

[66]  Mario Di Paola,et al.  A discrete mechanical model of fractional hereditary materials , 2013 .

[67]  Qiang Chen,et al.  Bio-mimetic mechanisms of natural hierarchical materials: a review. , 2013, Journal of the mechanical behavior of biomedical materials.

[68]  N. Caille,et al.  Contribution of the nucleus to the mechanical properties of endothelial cells. , 2002, Journal of biomechanics.