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

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).