Dielectric relaxation model of human blood as a superposition of Debye functions with relaxation times following a Modified-Weibull distribution

Abstract

Dielectric spectroscopy of the human blood is a powerful and convenient non-invasive testing technique that can be used to diagnose diseases such as diabetes and leukemia. One needs to consider rigorous experimental procedures and mathematical models to make the results of this type of test comparable. The present paper will discuss previously published results to further investigate the statistical modeling of the dielectric properties of human blood. The analysis shows that previously published results were related to Modified Weibull (MW) distributions of relaxation times, not Gaussian distributions, as reported. This re-analysis prevents the ill definition of fitting parameters, making sure they present physically justifiable values. Besides, for fluids presenting a Modified Weibull distribution of relaxation times, novel exact and closed-form expressions for the real and imaginary parts of complex permittivities were obtained in terms of generalized hypergeometric functions. Also, a high accuracy approximation was built for the imaginary part of the complex permittivity, creating an easy-to-use alternative expression for practitioners. The new results are used to fit experimental results for human blood, showing that more robust estimators are built for the parameters involved, which can be used as thresholds to classify the dielectric behavior of blood as normal (healthy) or anomalous (sick).

Electrodeformation of White Blood Cells Enriched with Gold Nanoparticles

“…This was accomplished by keeping the voltage constant at 10V while varying the signal frequency and measuring the time needed for nearby cells to reach the electrode tip. This time is inversely related to the attractive force, and serves as a good initial approximation of the CM factor [28, 29]. Due to the design of our device, negative DEP forces are very small, and this method fails as the frequency approaches the cell’s crossover value and time goes to “infinity”.…”

“…We have used output of this model and the prescription offered by [29] to generate the plot in the Fig. 4.…”

FDTD-Based Electromagnetic Modeling of Dielectric Materials with Fractional Dispersive Response

“…A modified Havriliak-Negami relationship has recently recently proposed with the aim of fitting experimental data exhibiting a two-power-law relaxation pattern [63]. A dielectric relaxation model based on Debye functions with relaxation times following a modified Weibull distribution was illustrated in [78]. In the same paper, the authors derived a new closed-form expressions for the real and imaginary parts of complex permittivities in terms of generalized hypergeometric functions.…”

Electrodeformation of White Blood Cells Enriched with Gold Nanoparticles

“…We have used the output of this model and the prescription offered by [37] to generate the plot in Figure 4 (R), for the imaginary component of complex permittivity. The white blood cell parameters are available (references here and Supporting Materials), and approximating the influence of AuNPs as a change of the relativity permittivity of the medium WBCs is used for this experiment.…”