Hybrid modeling of electroporation and impedance spectroscopy for label free characterization of stem cells

Abstract Label-free, non-destructive characterization of stem-cell differentiation states remains an important goal in regenerative medicine and cell therapy. Existing computational frameworks commonly treat electroporation either at the tissue scale or for simplified single-cell geometries, and relatively few studies connect time-domain electroporation observables with swept-frequency impedance features measured in a microfluidic platform. This study presents a revised hybrid analytical–numerical and experimental framework for comparing undifferentiated human mesenchymal stem cells (hMSCs) with osteogenic-committed hMSCs. The numerical models are parameterized using the cell-type values : an undifferentiated hMSC model with representative radius $$R_{\textrm{U}}={10}\,\upmu \hbox {m}$$ , cytoplasmic conductivity $$\sigma _{i,\textrm{U}}={0.32}\,\hbox {S m}^{-1}$$ , membrane capacitance $$C_{m,\textrm{U}}=1\times 10^{-2}\,\hbox {F m}^{-2}$$ , and characteristic electroporation voltage $$U_{\textrm{ep,U}}={0.258}\,\text {V}$$ ; and an osteogenic hMSC model with $$R_{\textrm{O}}={13}\,\upmu \hbox {m}$$ , $$\sigma _{i,\textrm{O}}={0.24}\,\hbox {S m}^{-1}$$ , $$C_{m,\textrm{O}}=8\times 10^{-3}\,\hbox {F m}^{-2}$$ , and $$U_{\textrm{ep,O}}={0.32}\,\text {V}$$ . Both models are placed in the same microfluidic electrode environment and excited by electric-field pulses ( $${1}\,\hbox {kV cm}^{-1}$$ to $${5}\,\hbox {kV cm}^{-1}$$ , rise time 1 ns). The passive Schwan RC time constants are $${4.69\times 10^{-7}}\,\text {s}$$ for undifferentiated hMSCs and $${5.96\times 10^{-7}}\,\text {s}$$ for osteogenic hMSCs; the plotted post-threshold rise times are shorter, on the order of $${1\times 10^{-7}}\,\text {s}$$ to $${2\times 10^{-7}}\,\text {s}$$ . The passive polar transmembrane potentials at $${5}\,\hbox {kV cm}^{-1}$$ are approximately $${7.5}\,\text {V}$$ and 9.75 V, respectively. Swept-frequency impedance spectroscopy ( $${1}\,\hbox {kHz}$$ to $${1}\,\hbox {MHz}$$ ) performed on undifferentiated and osteogenic-committed hMSCs provides the matched frequency-domain comparison: low-frequency impedance, series resistance, reactance trough depth, phase angle, and voltage-dependent impedance drop are extracted at applied voltages of 1, 5, 10, 15, 20, and 25 V. The experimental data show that osteogenic hMSCs have higher baseline impedance ( $$|Z|={11029}\,\Omega$$ vs. $${7863}\,\Omega$$ at $${1}\,\text {V}$$ , $${1}\,\hbox {kHz}$$ ), whereas undifferentiated hMSCs exhibit the stronger high-voltage impedance drop at $${25}\,\text {V}$$ approximately (92.4 % compared with 86.9 % for osteogenic hMSCs). Calibrated 10.4  $$\upmu$$ m and 24.9  $$\upmu$$ m polystyrene microbeads are included as cell-free size standards for the impedance workflow. The combined results define a cell-type feature space $${\mathcal {F}}_{\textrm{combined}} = \{\tau _{\textrm{charge}},\; V_m,\; N(t),\; r_p(t),\; \sigma _m(t),\; f_c,\; \Delta |Z|_{f_{c,0}},\; R_{s,1\,\textrm{kHz}},\; |X_{s,\textrm{pk}}|\}$$ for future label-free classification studies. The present work should be interpreted as a matched modelling and impedance-analysis framework; definitive biological classification, direct pore imaging, viability validation, and trained classifier performance remain outside the scope of this study.