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Electric cell substrate impedance sensing has been widely used as a label free quantitative platform to study various cell biological processes and it is extremely essential to extract the parameters like the variation of the cell substrate spacing, changing projected area of the cell on the electrode and approximate cluster size during the non-confluent state to understand the mechanism of proliferation of the cells. The distributed analytical models developed so far to extract these parameters are applicable only under the conditions when the cells have become confluent. There are some lumped electrical models which have been reported for the non-confluent state but they do not provide correct estimate of the changing cell substrate spacing and the cell cluster size during growth. In this paper we develop extended distributed electrical models to characterize the impedance spectroscopy behavior of cultured HeLa cells in 200 Hz to 1 MHz range using eight well ECIS electrodes in the non-confluent state. The distributed model introduces some pseudo regularity in the arrangement of the non-confluent cells to extract the average ensemble of the significant parameters. The parameters extracted from the distributed model after 10 hours, 20 hours, and 30 hours of HeLa cell growth have been compared with the lumped circuit model and has been observed to fit the experimental data with a seven times improved fit quality factor. Further, the changing cell radius and cluster radius extracted at three different instants of time from the distributed analytical model have been found to match closely the microscopic observation in contrast to the lumped circuit model.