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A novel image reconstruction method called multiple regression fitting electrical impedance spectro-tomography (<italic>mrf</italic>-EIST) has been proposed in order to realize the quantitative image reconstruction of dead cell fraction <inline-formula> <tex-math notation="LaTeX">$\phi _{d}$ </tex-math></inline-formula> and cell concentration <inline-formula> <tex-math notation="LaTeX">$c_{c}$ </tex-math></inline-formula> in a huge amount of cell environment. <italic>mrf</italic>-EIST statistically selects frequencies to extract two variables <inline-formula> <tex-math notation="LaTeX">$\psi _{d}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\psi _{c}$ </tex-math></inline-formula>, which quantify<inline-formula> <tex-math notation="LaTeX">$\phi _{d}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$c_{c}$ </tex-math></inline-formula>, respectively. The <inline-formula> <tex-math notation="LaTeX">$\phi _{d}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$c_{c}$ </tex-math></inline-formula> images are reconstructed by solving the inverse problem using <inline-formula> <tex-math notation="LaTeX">$\psi _{d}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\psi _{c}$ </tex-math></inline-formula>. To validate the performance of <italic>mrf</italic>-EIST, the image reconstruction by <italic>mrf</italic>-EIST in the frequency range from 100 Hz to 1 MHz is carried out under the condition that the number of cells is over 10<sup>9</sup> cells. As a result, <italic>mrf</italic>-EIST shows that the image quality defined by the difference in pixel value from the true image is less than 0.050 in <inline-formula> <tex-math notation="LaTeX">$\phi _{d}$ </tex-math></inline-formula> and 0.071 in <inline-formula> <tex-math notation="LaTeX">$c_{c}$ </tex-math></inline-formula>, respectively. In comparison to frequency-difference EIT (<italic>fd</italic>-EIT) as a conventional EIST regarding a position error of center of gravity, <italic>mrf</italic>-EIST provides much more accurate images, qualitatively and quantitatively, compared to the <italic>fd</italic>-EIT.

Multiple Regression Fitting Electrical Impedance Spectro-Tomography for Quantitative Image Reconstruction of Dead Cell Fraction and Cell Concentration