Modelling effective dielectric properties of materials containing diverse types of biological cells

An efficient and versatile numerical method for the generation of different realistically shaped biological cells is developed. This framework is used to calculate the dielectric spectra of materials containing specific types of biological cells. For the generation of the numerical models of the cells a flexible parametrization method based on the so-called superformula is applied including the option of obtaining non-axisymmetric shapes such as box-shaped cells and even shapes corresponding to echinocytes. The dielectric spectra of effective media containing various cell morphologies are calculated focusing on the dependence of the spectral features on the cell shape. The numerical method is validated by comparing a model of spherical inclusions at a low volume fraction with the analytical solution obtained by the Maxwell‐Garnett mixing formula, resulting in good agreement. Our simulation data for different cell shapes suggest that around 1MHz the effective dielectric properties of different cell shapes at different volume fractions significantly deviate from the spherical case. The most pronounced change exhibits ! eff between 0.1 and 1MHz with a deviation of up to 35% for a box-shaped cell and 15% for an echinocyte compared with the sphere at a volume fraction of 0.4. This hampers the unique interpretation of changes in cellular features measured by dielectric spectroscopy when simplified material models are used. (Some figures in this article are in colour only in the electronic version)

[1]  Koji Asami,et al.  Characterization of heterogeneous systems by dielectric spectroscopy , 2002 .

[2]  G. Fuhr,et al.  Dielectric spectroscopy of single human erythrocytes at physiological ionic strength: dispersion of the cytoplasm. , 1996, Biophysical journal.

[3]  C. Cametti,et al.  Dielectric spectroscopy of erythrocyte cell suspensions. A comparison between Looyenga and Maxwell-Wagner-Hanai effective medium theory formulations , 2002 .

[4]  V. Raicu,et al.  Non-Debye dielectric relaxation in biological structures arises from their fractal nature. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  D. Kell,et al.  The passive electrical properties of biological systems: their significance in physiology, biophysics and biotechnology. , 1987, Physics in medicine and biology.

[6]  J. L. Sebastian,et al.  Electric field distribution and energy absorption in anisotropic and dispersive red blood cells , 2007, Physics in medicine and biology.

[7]  Hywel Morgan,et al.  Broadband single cell impedance spectroscopy using maximum length sequences: theoretical analysis and practical considerations , 2007 .

[8]  Andres J Klein-Szanto.  Clear and Dark Basal Keratinocytes in Human Epidermis , 1977, Journal of cutaneous pathology.

[9]  Elise C. Fear,et al.  Modeling assemblies of biological cells exposed to electric fields , 1998 .

[10]  A. Yasuda,et al.  Dielectric cytometry with three-dimensional cellular modeling. , 2008, Biophysical journal.

[11]  Victor N. Kaliakin,et al.  Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods , 2001 .

[12]  C. Cametti,et al.  Effect of shape on the dielectric properties of biological cell suspensions. , 2007, Bioelectrochemistry.

[13]  T. Tamura,et al.  Modelling of the dielectric properties of normal and irradiated skin. , 1994, Physics in medicine and biology.

[14]  Y. Istefanopulos,et al.  IEEE Engineering in Medicine and Biology Society , 2019, IEEE Transactions on Biomedical Engineering.

[15]  Jan Gimsa,et al.  Dielectric anisotropy, volume potential anomalies and the persistent Maxwellian equivalent body , 2005 .

[16]  Koji Asami,et al.  Dielectric dispersion in biological cells of complex geometry simulated by the three-dimensional finite difference method , 2006 .

[17]  L. Dissado,et al.  A fractal interpretation of the dielectric response of animal tissues. , 1990, Physics in medicine and biology.

[18]  Paul Geladi,et al.  Non‐invasive and microinvasive electrical impedance spectra of skin cancer – a comparison between two techniques , 2005, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[19]  P Jack Hoopes,et al.  In vivo EIS characterization of tumour tissue properties is dominated by excess extracellular fluid , 2007, Physics in medicine and biology.

[20]  Sunghee Choi,et al.  The power crust , 2001, SMA '01.

[21]  M. Tabrizian,et al.  Complex permittivity measurement as a new noninvasive tool for monitoring in vitro tissue engineering and cell signature through the detection of cell proliferation, differentiation, and pretissue formation , 2004, IEEE Transactions on NanoBioscience.

[22]  Dominique Barchiesi,et al.  Models of near-field spectroscopic studies: comparison between Finite-Element and Finite-Difference methods. , 2005, Optics express.

[23]  M.A. Stuchly,et al.  Modeling assemblies of biological cells exposed to electric fields , 1997, IEEE Transactions on Biomedical Engineering.

[24]  Charles Polk,et al.  CRC Handbook of Biological Effects of Electromagnetic Fields , 1986 .

[25]  Mark S. Talary,et al.  In vivo life sign application of dielectric spectroscopy and non-invasive glucose monitoring , 2007 .

[26]  F. Barnes,et al.  Handbook of biological effects of electromagnetic fields , 2007 .

[27]  Neil A. Rowson,et al.  Dielectric properties of coal , 2001 .

[28]  V. Raicu,et al.  A quantitative approach to the dielectric properties of the skin. , 2000, Physics in medicine and biology.

[29]  Holger Steeb,et al.  Comparison of finite difference and finite element methods for simulating two-dimensional scattering of elastic waves , 2008 .

[30]  Nanoscale devices for online dielectric spectroscopy of biological cells. , 2008, Physiological measurement.

[31]  D R Hose,et al.  Modelled current distribution in cervical squamous tissue. , 2002, Physiological measurement.

[32]  Stanislaw Gubanski,et al.  Dielectric relaxation in dielectric mixtures: Application of the finite element method and its comparison with dielectric mixture formulas , 2001 .

[33]  D Miklavcic,et al.  Theoretical evaluation of the distributed power dissipation in biological cells exposed to electric fields. , 2000, Bioelectromagnetics.

[34]  D M Ferreira,et al.  Electrical impedance model for evaluation of skin irritation in rabbits and humans , 2007, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[35]  O. Dössel,et al.  CALCULATION OF THE DIELECTRIC PROPERTIES OF BIOLOGICAL TISSUE USING SIMPLE MODELS OF CELL PATCHES , 2002, Biomedizinische Technik. Biomedical engineering.

[36]  Jonathon Howard,et al.  Shapes of Red Blood Cells: Comparison of 3D Confocal Images with the Bilayer-Couple Model , 2008, Cellular and molecular bioengineering.

[37]  Effective dielectric properties of biological cells: generalization of the spectral density function approach. , 2009, The journal of physical chemistry. B.

[38]  S Muñoz San Martín,et al.  Modeling normal and altered human erythrocyte shapes by a new parametric equation: application to the calculation of induced transmembrane potentials. , 2006, Bioelectromagnetics.

[39]  Johan Gielis,et al.  Superquadrics with rational and irrational symmetry , 2003, SM '03.

[40]  R. W. Lau,et al.  The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. , 1996, Physics in medicine and biology.

[41]  K. Asami.  Simulation of dielectric spectra of erythrocytes with various shapes , 2009 .

[42]  C. Cametti,et al.  Numerical simulation of dielectric spectra of aqueous suspensions of non-spheroidal differently shaped biological cells , 2009 .

[43]  Koji Asami,et al.  Characterization of biological cells by dielectric spectroscopy , 2002 .

[44]  S W Smye,et al.  Modelling the electrical properties of tissue as a porous medium , 2007, Physics in medicine and biology.

[45]  Comparison of Finite-Difference and Finite-Element Schemes for Magnetization Processes in 3-D Particles , 2009, IEEE Transactions on Magnetics.

[46]  R. Mukhopadhyay,et al.  Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: Evidence for the bilayer– couple hypothesis from membrane mechanics , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[47]  E Marzec,et al.  The electrical properties of leg skin in normal individuals and in patients with ischemia. , 1999, Bioelectrochemistry and bioenergetics.

[48]  Eugen Gheorghiu,et al.  Dielectric behaviour of gap junction connected cells: a microscopic approach. , 2002, Physics in medicine and biology.

[49]  Valerica Raicu,et al.  Dielectric properties of rat liver in vivo: analysis by modeling hepatocytes in the tissue architecture , 1998 .

[50]  Ari Sihvola,et al.  Electromagnetic mixing formulas and applications , 1999 .

[51]  S. Gawad,et al.  Single cell dielectric spectroscopy , 2007 .

[52]  Sonja Huclova,et al.  Validation of human skin models in the MHz region , 2009, 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[53]  J L Sebastián,et al.  Analysis of the influence of the cell geometry, orientation and cell proximity effects on the electric field distribution from direct RF exposure. , 2001, Physics in medicine and biology.

[54]  J. Mönkkönen,et al.  Measurement of oedema in irritant‐exposed skin by a dielectric technique , 2006, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[55]  Jonathon Howard,et al.  Spherical harmonics-based parametric deconvolution of 3D surface images using bending energy minimization , 2008, Medical Image Anal..

[56]  K. Zhao,et al.  Dielectric properties of E. coli cell as simulated by the three-shell spheroidal model. , 2006, Biophysical chemistry.

[57]  K. Yu,et al.  First-principle approach to dielectric behavior of nonspherical cell suspensions. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  F. Stillinger,et al.  Improving the Density of Jammed Disordered Packings Using Ellipsoids , 2004, Science.

[59]  J. Gielis.  A generic geometric transformation that unifies a wide range of natural and abstract shapes. , 2003, American journal of botany.