Skip to main content

Mechanical-Mathematical Modelling of Biological Tissue Behaviour

  • Conference paper
  • First Online:
Analytic Methods in Interdisciplinary Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 116))

Abstract

In present work mechanics-mathematical models are constructed to define physical and mechanical properties of biological tissue. These models were adapted to the AFM experimental data so to be a theoretical basis for one. Researched theoretical results are compared with experimental data to confirm sufficiently high level adequacy of offered methodology for definition of physical and mechanical properties biotissue.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. G.I. Mchedlishvili, Microcirculation, 3rd edn. (Nauka, Leningrad, 1989)

    Google Scholar 

  2. K.E. Bremmell, A. Evans, A. Clive, Prestidge Deformation and Nano-rheology of Red Blood Cells: an AFM Investigation. Colloids Surf. B: Biointerfaces (2006)

    Google Scholar 

  3. Chien S., What is clinical haemorheology? Royal Society of Medicine Services Limited. International Congress and Symposium Series: Clinical haemorheology: A New Approach toCerebrovascular Disease, vol. 100 (1986), pp. 3–9

    Google Scholar 

  4. G.R. Cokelet, H.J. Meiselman, D.E. Brooks, Erythrocyte Mechanics and Blood Flow (Liss, New York, 1980)

    Google Scholar 

  5. H. Hertz, Ueber den kontaktelastischerkoerper. J. fuer die ReineAngewandteMathematik 92 (1881)

    Google Scholar 

  6. L. Sirghi, J. Ponti, F. Broggi, Probing elasticity and adhesion of live cells by atomic force microscopy indentation. EurBiophys. J. 37, 935–945 (2008)

    Google Scholar 

  7. S.A. Chizhik, Z. Huang, V.V. Gorbunov, Micromechanical properties of elastic polymeric materials as probed by scanning force microscopy. Langmuir 14, 2606–2609 (1998)

    Article  Google Scholar 

  8. B.J. Lincoln et al., Deformability-based flow cytometry. Cytometry, Part A 59, 203–209 (2004)

    Article  Google Scholar 

  9. E.C. Faria et al., Measurement of elastic properties of prostate cancer cells using AFM. Analyst 133(11), 1498–1500 (2008)

    Article  Google Scholar 

  10. M. Lekka et al., Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy. Eur. Biophys. J. 28, 312–316 (1999)

    Article  Google Scholar 

  11. K.A. Ward et al., Viscoelastic properties of transformed cells: role in tumor cell progression and metastasis formation. Biorheology 28, 301–313 (1991)

    Google Scholar 

  12. A.A. Askadskii, Deformation of Polymers (Chemistry, Moscow, 1973)

    Google Scholar 

  13. V.P. Sverbil, S.D. Zaharov, Erythrocytes in a shift stream: deformability mechanisms, methods of measurements, medical applications. XV International Conference "Mathematics Computer Education", vol. 3 ( Igevsk, Moscow 2008), pp. 123–130

    Google Scholar 

  14. E. Canetta et al., Measuring cell viscoelastic properties using a force-spectrometer: influence of protein-cytoplasm interactions. Biorheology 42, 321–333 (2005)

    Google Scholar 

  15. M.N. Starodubtseva, Mechanical properties of cells and ageing. Ageing Res. Rev. 10 (2001)

    Google Scholar 

  16. H. Strey, M. Peterson, E. Sackmann, Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. Biophys. J. 69, 478–488 (1995)

    Article  Google Scholar 

  17. Applied Biophysics: A Molecular Approach for Physical Scientists. (Chichester, Hoboken, 2007)

    Google Scholar 

  18. G. Massiera, Mechanics of single cells: rheology, time dependence, and fluctuations. Biophys. J. 93, 3703–3713 (2007)

    Article  Google Scholar 

  19. A.A. Tager, Physics-Chemistry of Polymers (Chemistry, Moscow, Russian, 1968)

    Google Scholar 

  20. V.A. Rudniskii, A.P. Kren, Test of elastomeric materials by indentirovaniye methods. Minsk, Belarus. Science (2007) (in Russian)

    Google Scholar 

  21. L.V. Snegireva, V.P. Ivanov, Rheological properties of erythrocytes in their ontogenesis. Person Health 1, 35–44 (2007)

    Google Scholar 

  22. R.P. Rand, Mechanical properties of the cell membrane. I. Membrane stiffness and intracellular pressure. Biophys. J. 4, 115–135 (1964)

    Article  Google Scholar 

  23. P.L. LaCelle, Alternations of deformability of the erythrocytes membrane in stored blood. Transfusion 9, 238–245 (1969)

    Article  Google Scholar 

  24. E.A. Ewans, Elastic area compressibility modulus of red cell membrane. Biophys. J. 16, 585–595 (1976)

    Article  Google Scholar 

  25. R. Waugh, Viscoelastic properties of erythrocyte membranes of different vertebrate animals. Microvasc. Res. 12, 291–304 (1976)

    Article  Google Scholar 

  26. G.B. Nash, Erythrocyte membrane elasticity during in vivo ageing. Biochim. et Biophys. Acta 643, 269–275 (1981)

    Article  Google Scholar 

  27. T. Bohler, Mechanical fragility of erythrocyte membrane in neonates and adults. Pediatr. Res. Acta 32, 92–96 (1992)

    Article  Google Scholar 

  28. R.M. Hochmuth, Measurement of the elastic modulus for red cell membrane using a fluid mechanical technique. Biophys. J. 13, 747–762 (1973)

    Article  Google Scholar 

  29. C. Maggakis-Kelemen, Determination of the elastic shear modulus of cultured human red blood cells. Biomed. Tech. 47, 106–109 (2002)

    Article  Google Scholar 

  30. G.M. Baerlocher, Erythrocyte deformability has no influence on the rate of erythrophagocytosis in vitro by autologous human monocytes/macrophages. Brit. J. Haematol. 86, 629–634 (1994)

    Article  Google Scholar 

  31. R.J. Rasia, Blood preservation bacteriological, immunohematological, hematological and hemorrheological studies. Sangre 43, 71–76 (1998)

    Google Scholar 

  32. R.B. Tishler, A study of the dynamic properties of the human red blood cell membrane using quasi-elastic light-scattering spectroscopy. Biophys. J. 43, 2586–2600 (1993)

    Article  Google Scholar 

  33. K. Fricke, Variation of frequency spectrum of the erythrocyte flickering caused by ageing, osmolarity, temperature and pathological changes. Biochim. et Biophys. Acta. 43, 145–152 (1984)

    Article  Google Scholar 

  34. M. Baumann, Cell ageing for 1 day alters both membrane elasticity and viscosity. Pflugers Arch. 445, 551–555 (1984)

    Google Scholar 

  35. R. Yip et al., Red cell membrane stiffness in iron deficiency. Blood 62, 99–106 (1983)

    Google Scholar 

  36. F.H. Bosch et al., Determinants of red blood cell deformability in relation to cell age. Europ. J. Haematol. 52, 35–41 (1983)

    Article  Google Scholar 

  37. T. Kaneta, An optical channel: a technique for the evaluation of biological cell elasticity. Anal. Chem. 24, 5791–5795 (2001)

    Article  Google Scholar 

  38. N. Caille et al., Contribution of the nucleus to the mechanical properties of endothelial cells. J. Biomech. 35, 177–187 (2002)

    Article  Google Scholar 

  39. J.C. Berrios, Mechanical properties of alveolar epithelial cells in culture. J. Appl. Physiol. 91, 65–73 (2001)

    Google Scholar 

  40. Y. Tseng, Micromechanical mapping of live cells by multiple-particle-tracking microrheology. Biophys. J. 83, 3162–3176 (2002)

    Article  Google Scholar 

  41. V.M. Laurent et al., Partitioning of cortical and deep cytoskeleton responses from transient magnetic bead twisting. Ann. Biomed. Eng. 31, 1263–1278 (2003)

    Article  MathSciNet  Google Scholar 

  42. A.C. Rowat, Mechanical properties of the cell nucleus and the effect of emerin deficiency. Biophys. J. 91, 4649–4664 (2006)

    Article  Google Scholar 

  43. C. Li, Nanomechanical characterization of red blood cells using optical tweezers. J. Mater. Sci. Mater. Med. 19, 1529–1535 (2008)

    Article  Google Scholar 

  44. L. Scheffer et al., Atomic force pulling: probing the local elasticity of the cell membrane. Eur. Biophys. J. 30, 83–90 (2001)

    Article  Google Scholar 

  45. R.E. Mahaffy et al., Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy. Biophys. J. 86, 1777–1793 (2004)

    Article  Google Scholar 

  46. B.A. Smith et al., Probing the viscoelastic behavior of cultured airway smooth muscle cells with atomic force microscopy: stiffening induced by contractile agonist. Biophys. J. 88, 2994–3007 (2005)

    Article  Google Scholar 

  47. T.K. Berdyyeva, Human epithelial cells increase their rigidity with ageing in vitro: direct measurements. Phys. Med. Biol. 50, 81–92 (2005)

    Article  Google Scholar 

  48. I. Sokolov, Recovery of elasticity of aged human epithelial cells in vitro. Nanomedicine 2, 31–36 (2006)

    Article  Google Scholar 

  49. K.D. Costa, Non-Hertzian approach to analyzing mechanical properties of endothelial cells probed by atomic force microscopy. J. Biomech. Eng. 128, 176–184 (2006)

    Article  Google Scholar 

  50. M.J. Rosenbluth, Force microscopy of nonadherent cells: a comparison of leukemia cell deformability. Biophys. J. 90, 2994–3003 (2006)

    Article  Google Scholar 

  51. S.N. Pleskova et al., Study of morphology and rigidity of neutrophilic granulocyte membrane in the real time mode by scanning probe microscopy. Bull. Exp. Biol. Med. 141, 760–762 (2005)

    Article  Google Scholar 

  52. M.N. Starodubtseva, Effect of peroxynitrite on mechanical properties of human erythrocyte membranes. Bull. Exp. Biol. Med. 143, 264–267 (2007)

    Article  Google Scholar 

  53. M.N. Starodubtseva et al., Structural and functional changes in the membrane and membrane skeleton of red blood cells induced by peroxynitrite. Bioelectrochemistry 73, 155–162 (2008)

    Article  Google Scholar 

  54. L. Sirghi et al., Probing elasticity and adhesion of live cells by atomic force microscopy indentation. Eur. Biophys. J. 37, 935–945 (2008)

    Article  Google Scholar 

  55. C. Roduit et al., Elastic membrane heterogeneity of living cells revealed by stiff nanoscale membrane domains. Biophys. J. 94, 1521–1532 (2008)

    Article  Google Scholar 

  56. R.E. Mahaffy et al., Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy. Biophys. J. 86, 1777–1793 (2004)

    Article  Google Scholar 

  57. B.A. Smith et al., Probing the viscoelastic behavior of cultured airway smooth muscle cells with atomic force microscopy: stiffening induced by contractile agonist. Biophys. J. 88, 2994–3007 (2005)

    Article  Google Scholar 

  58. M.N. Starodubtseva et al., Atomic force microscopy observation of peroxynitrite-induced erythrocyte cytoskeleton reorganization. Micron 38, 782–786 (2007)

    Article  Google Scholar 

  59. S. Paramore et al., Extending a spectrin repeat unit. I: Linear force-extension response. Biophys. J. 90, 92–100 (2006)

    Article  Google Scholar 

  60. T.G. Kyznecova, AFM elastography—new method of biomedical research. Probl. Heath Ecol. 1.15, 143–150 (2008)

    Google Scholar 

  61. S. Sasaki et al., Elastic properties of living fibroblasts as imaged using force modulation mode in atomic force microscopy. Arch. Histol. 2nd Cytol. 61, 57–63 (1998)

    Article  Google Scholar 

  62. M. Nagayama, Drastic change of local stiffness distribution correlating to cell migration in living fibroblasts. Cell Motil. Cytoskelet. 50, 173–179 (2001)

    Article  Google Scholar 

  63. H. Haga et al., Time-lapse viscoelastic imaging of living fibroblasts using force modulation mode in AFM. J. Electron. Microsc. 49, 473–481 (2000)

    Article  Google Scholar 

  64. A.M. Collinsworth et al., Apparent elastic modulus and hysteresis of skeletal muscle cells throughout differentiation Amer. J. Physiol. Cell Physiol. 283, 1219–1227 (2002)

    Article  Google Scholar 

  65. S. Zhang, Stretch-induced nitric oxide modulates mechanical properties of skeletal muscle cells. Am. J. Physiol. Cell Physiol. 287, 292–299 (2004)

    Article  Google Scholar 

  66. W.E. Brownell et al., Micro- and nanomechanics of the cochlear outer hair cell. Annu. Rev. Biomed. Eng. 287, 169–194 (2001)

    Article  Google Scholar 

  67. S.C. Lieber et al., Aging increases stiffness of cardiac myocytes measured by atomic force microscopy nanoindentation. Amer. J. Physiol. Heart Circ. Physiol. 287, 645–651 (2004)

    Article  Google Scholar 

  68. H. Sato et al., Kinetic study on the elastic change of vascular endothelial cells on collagen matrices by atomic force microscopy. Colloids Surf. B: Biointerf. 34, 141–146 (2004)

    Article  Google Scholar 

  69. E. Takai et al., Osteoblast elastic modulus measured by atomic force microscopy is substrate dependent. Ann. Biomed. Eng. 33, 963–971 (2005)

    Article  Google Scholar 

  70. A. Simon et al., Characterization of dynamic cellular adhesion of osteoblasts using atomic force microscopy. Cytometry Pt. A 54, 36–47 (2003)

    Article  Google Scholar 

  71. J. Domke et al., Substrate dependent differences in morphology and elasticity of living osteoblasts investigated by atomic force microscopy. Colloids Surf. B: Biointerf. 19, 367–379 (2000)

    Article  Google Scholar 

  72. M. Fritz, Granula motion and membrane spreading during activation of human platelets imaged by atomic force microscopy. Colloids Surf. B: Biointerf. 66, 1328–1334 (1994)

    Google Scholar 

  73. M. Fritz, In vitro activation of human plateles triggered and probed by atomic force microscopy. Exp. Cell Res. 205, 187–190 (1995)

    Article  Google Scholar 

  74. P. Hinterdorfer, Detection and localization of single molecular recognition events using atomic force microscopy. Nat. Methods 3, 347–355 (2006)

    Article  Google Scholar 

  75. D.J. Frankel et al., Revealing the topography of cellular membrane domains by combined atomic force microscopy/fluorescence imaging. Biophys. J. 90, 2404–2413 (2006)

    Article  Google Scholar 

  76. Z. Liv et al., Imaging recognition events between human IgG and rat anti-human IgG by atomic force microscopy. Int. J. Biol. Macromol. 47, 661–667 (2010)

    Article  Google Scholar 

  77. T.S. Tsapikouni, Y.F. Missirlis, Measuring the force of single protein molecule detachment from surfaces with AFM. Colloids Surf. B: Biointerf. 75, 2529–2599 (2010)

    Article  Google Scholar 

  78. H. Sekiguchi et al., High-sensitivity detection of proteins using gel electrophoresis and atomic force microscopy. Ultramicroscopy 109, 916–922 (2009)

    Article  Google Scholar 

  79. N. Burnham, R.J. Colton, Measuring the nanomechanical properties and surface forces of materials using an atomic force microscope. J. Vac. Sci. Technol. A7, 2906–2913 (1989)

    Article  Google Scholar 

  80. T.G. Kuznetsova et al., Atomic force microscopy probing of cell elasticity. Micron 38, 824–833 (2007)

    Article  Google Scholar 

  81. X. Cai et al., Connection between biomechanics and cytoskeleton structure of Iymphocyte and jurkat cells: an AFM study. Micron 41, 257–262 (2010)

    Article  Google Scholar 

  82. M. Radmacher et al., Measuring the viscoelastic properties of human platelets with the atomic force microscope. Biophys. J. 70, 556–567 (1996)

    Article  Google Scholar 

  83. A.M. Frendental, H. Geiringer, The Mathematical Theories of the Inelastic Continuum 3Handbuch der Physik, Bd. VI., (Springer, Berlin, Giittingen, Heidelberg 1958)

    Google Scholar 

  84. M. Zhuravkov, N. Romanova, Review of methods and approaches for mechanical problem solutions based on fractional calculus. Math. Mech. Solids. 1–26. doi:10.1177/1081286514533340

  85. A. Gefen, Cellular and biomolecular mechanics and mechanobiology series. Stud. Mechanobiol. Tissue Eng. Biomater. 4, 4–560 (2011)

    Google Scholar 

  86. M. Zhuravkov, Fundamental Solutions of Elastic Theory and Some Their Applications in Geomechanics, Soil and Bases Mechanics (BSU, Minsk, 2008)

    Google Scholar 

  87. S.P. Timoshenko, Theory of Plates and Shells (McGraw-Hill, New-York, 1970)

    Google Scholar 

  88. M.M. Gibbons, Nonlinear finite-element analysis of nanoindentation of viral capsids. Biophys. J. 90, 1817–1828 (2006)

    Google Scholar 

  89. F. Horkay, Physical Properties of Polymers, Handbook New York (2007)

    Google Scholar 

  90. D.C. Lin, Elasticity of rubber-like materials measured by AFM nanoindentation. Express Polymer Lett. 1, 576–584 (2009)

    Article  Google Scholar 

  91. R.W. Ogden, Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 326, pp. 565–584 (1972)

    Google Scholar 

  92. Y.C. Fung, Elasticity of soft tissues in simple elongation. Am. J. Physiol. 213, 1532–1544 (1967)

    Google Scholar 

  93. R.J. Gaylord, Robber elasticity: a scaling approach. Polymer Bull. 18, 347–354 (1987)

    Article  Google Scholar 

  94. N.W. Tschoegl, C. Gurer, Behavior of elastomer networks inmoderately large deformations.1. Elastic equilibrium. Polymer Bull. 18, 347–354 (1987)

    Google Scholar 

  95. H.G. Kilian, An interpretation of the strain-invariants in largely strained networks. Colloid Polymer Sci. 263, 30–34 (1985)

    Article  Google Scholar 

  96. K.L. Johnson, Mechanics of Contact Interaction (Word, Moscow, 1987)

    Google Scholar 

  97. S.O. Abetkovskay, S.A. Chigik, Dynamic Power Spectroscopy of Soft Materials. (Minsk 2007)

    Google Scholar 

  98. A. Alessandrini, AFM: a versatile tool in biophysics. Meas. Sci. Technol. 16, R65–R92 (2005)

    Article  Google Scholar 

  99. M. Salerno, I. Bykov, Tutorial: mapping adhesion forces and calculating elasticity in contract-mode AFM. Microsc. Anal. 20, S5–S8 (2006)

    Google Scholar 

  100. M. Zhuravkov, Fundamental Solutions of Elastic Theory and Some Their Applications in Geomechanics, Soil and Bases Mechanics (BSU, Minsk, 2008)

    Google Scholar 

  101. M.A. Zhuravkov et al., Strength and fracture of deformable media under dynamic loads. Mech. Constr. Mech. 3, 35–43 (2008) (in Russian)

    Google Scholar 

  102. I.I. Argatov, F.J. Sabina, Asymptotic analysis of the substrate effect for an arbitrary indenter. (2012). doi: arXiv:1207.1471v1 [math.Ap]

  103. I.I. Argatov, Depth-sensing indentation of a transversely elastic layer: second-order asymptotic models for canonical indenters. Int. J. Solods Struct. 48, 3444–3452 (2011)

    Article  Google Scholar 

  104. A.V. Krupoderov, Green Functions for Transversely Isotropic Bases, vol. 3, (Vestnik, BNTU, 2011)

    Google Scholar 

  105. M. Zhuravkov, E.I. Staravoitov, Continua Mechanics (Theory elasticity and plasticity Minsk, BSU, 2011)

    Google Scholar 

  106. A.G. Gorskov et al., Waves Continous Media (FIZMATLIT, Moscow, 2004)

    Google Scholar 

  107. E. Drozd, G. Mikhasev, S. Chizhik, Evaluation of the local elasticity modulus of biological cells on the basis of the shells theory. Ser. Biomech. 27, 17–22 (2012)

    Google Scholar 

  108. G.I. Mchedlishvili, Microcirculation. (Leningrad, Nauka 1989) (in Russian)

    Google Scholar 

  109. K.E. Bremmell, A. Evans, A. Clive, Prestidge deformation and nano-rheology of red blood cells: An AFM investigation. Colloids Surf. B: Biointerfaces 50, 43–48 (2006)

    Article  Google Scholar 

  110. Chien S., What is clinical haemorheology? Royal Society of Medicine Services Limited. International Congress and Symposium Series: Clinical haemorheology: A New Approach toCerebrovascular Disease, vol. 100 (1986), pp. 3–9

    Google Scholar 

  111. H.J. Meiselman, G.R. Cokelet, D.E. Brooks, Measures of Blood Rheology and Erythrocyte Mechanics (New York, 1980), pp. 75–117

    Google Scholar 

  112. L. Sirghi, J. Ponti, F. Broggi, Probing elasticity and adhesion of live cells by atomic force microscopy indentation. EurBiophys. J. 37, 935–945 (2008)

    Google Scholar 

  113. S.A. Chizhik, Z. Huang, V.V. Gorbunov, Micromechanical properties of elastic polymeric materials as probed by scanning force microscopy. Langmuir 14, 2606–2609 (1998)

    Article  Google Scholar 

  114. E.S. Drozd, S.A. Chizhik, E.E. Kontantinova, Mechanical characteristics of erythrocyte membranes in patients with type 2 diabetes mellitus. Ser. Biomech. Bulg. Soc. Biomech. 25, 53–60 (2010)

    Google Scholar 

  115. E.S. Drozd et al., Probing mechanical and structural properties of the erythrocyte membrane by atomic force microscopy. Russ. J. Biomech. 13, 22–30 (2009) (in Russian)

    Google Scholar 

  116. B. Lincoln et al., Deformability-based flow cytometry, Part A, 59 (2004), 203–209

    Google Scholar 

  117. E.C. Faria et al., Measurement of elastic properties of prostate cancer cells using AFM. Analysts 113, 1498–1500 (2008)

    Article  Google Scholar 

  118. M. Starodubtseva et al., Study of the mechanical properties of single cells as biocomposites by atomic force microscopy. Microscopy: Science, Technology, Applications and Education: [in 3 vol.], vol. 1 (Formatex Research Center, Badajoz, 2010), pp. 470–477

    Google Scholar 

  119. M. Lekka et al., Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy. Eur. Biophys. J. 28, 312–316 (1999)

    Article  Google Scholar 

  120. K.A. Ward et al., Viscoelastic properties of transformed cells: role in tumor cell progression and metastasis formation. Biorheology 28, 301–313 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Zhuravkov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Zhuravkov, M., Drozd, L., Romanova, N., Krupoderov, A. (2015). Mechanical-Mathematical Modelling of Biological Tissue Behaviour. In: Mityushev, V., Ruzhansky, M. (eds) Analytic Methods in Interdisciplinary Applications. Springer Proceedings in Mathematics & Statistics, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-12148-2_9

Download citation

Publish with us

Policies and ethics