<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_{\textrm{U}}={10}\,\upmu \hbox {m}\)</EquationSource> </InlineEquation>, cytoplasmic conductivity <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma _{i,\textrm{U}}={0.32}\,\hbox {S m}^{-1}\)</EquationSource> </InlineEquation>, membrane capacitance <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C_{m,\textrm{U}}=1\times 10^{-2}\,\hbox {F m}^{-2}\)</EquationSource> </InlineEquation>, and characteristic electroporation voltage <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(U_{\textrm{ep,U}}={0.258}\,\text {V}\)</EquationSource> </InlineEquation>; and an osteogenic hMSC model with <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(R_{\textrm{O}}={13}\,\upmu \hbox {m}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\sigma _{i,\textrm{O}}={0.24}\,\hbox {S m}^{-1}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(C_{m,\textrm{O}}=8\times 10^{-3}\,\hbox {F m}^{-2}\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(U_{\textrm{ep,O}}={0.32}\,\text {V}\)</EquationSource> </InlineEquation>. Both models are placed in the same microfluidic electrode environment and excited by electric-field pulses (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\({1}\,\hbox {kV cm}^{-1}\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\({5}\,\hbox {kV cm}^{-1}\)</EquationSource> </InlineEquation>, rise time 1&#xa0;ns). The passive Schwan RC time constants are <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\({4.69\times 10^{-7}}\,\text {s}\)</EquationSource> </InlineEquation> for undifferentiated hMSCs and <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\({5.96\times 10^{-7}}\,\text {s}\)</EquationSource> </InlineEquation> for osteogenic hMSCs; the plotted post-threshold rise times are shorter, on the order of <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\({1\times 10^{-7}}\,\text {s}\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\({2\times 10^{-7}}\,\text {s}\)</EquationSource> </InlineEquation>. The passive polar transmembrane potentials at <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\({5}\,\hbox {kV cm}^{-1}\)</EquationSource> </InlineEquation> are approximately <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\({7.5}\,\text {V}\)</EquationSource> </InlineEquation> and 9.75&#xa0;V, respectively. Swept-frequency impedance spectroscopy (<InlineEquation ID="IEq17"> <EquationSource Format="TEX">\({1}\,\hbox {kHz}\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\({1}\,\hbox {MHz}\)</EquationSource> </InlineEquation>) 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&#xa0;V. The experimental data show that osteogenic hMSCs have higher baseline impedance (<InlineEquation ID="IEq19"> <EquationSource Format="TEX">\(|Z|={11029}\,\Omega\)</EquationSource> </InlineEquation> vs. <InlineEquation ID="IEq20"> <EquationSource Format="TEX">\({7863}\,\Omega\)</EquationSource> </InlineEquation> at <InlineEquation ID="IEq21"> <EquationSource Format="TEX">\({1}\,\text {V}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq22"> <EquationSource Format="TEX">\({1}\,\hbox {kHz}\)</EquationSource> </InlineEquation>), whereas undifferentiated hMSCs exhibit the stronger high-voltage impedance drop at <InlineEquation ID="IEq23"> <EquationSource Format="TEX">\({25}\,\text {V}\)</EquationSource> </InlineEquation> approximately (92.4&#xa0;% compared with 86.9&#xa0;% for osteogenic hMSCs). Calibrated 10.4&#xa0;<InlineEquation ID="IEq24"> <EquationSource Format="TEX">\(\upmu\)</EquationSource> </InlineEquation>m and 24.9&#xa0;<InlineEquation ID="IEq25"> <EquationSource Format="TEX">\(\upmu\)</EquationSource> </InlineEquation>m polystyrene microbeads are included as cell-free size standards for the impedance workflow. The combined results define a cell-type feature space <InlineEquation ID="IEq26"> <EquationSource Format="TEX">\({\mathcal {F}}_{\textrm{combined}} = \{\tau _{\textrm{charge}},\; V_m,\; N(t),\; r_p(t),\; \sigma _m(t),\; f_c,\; \Delta |Z|_{f_{c,0}},\; R_{s,1\,\textrm{kHz}},\; |X_{s,\textrm{pk}}|\}\)</EquationSource> </InlineEquation> 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.</p>

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

  • Sameh Sherif,
  • Yehya H. Ghallab,
  • Yehea Ismail

摘要

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.