{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T08:12:53Z","timestamp":1788336773386,"version":"build-2803163510"},"reference-count":38,"publisher":"SAGE Publications","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Biomed Eng Comput Biol"],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Classical integer-order membrane and bioelectrical circuit models are useful for idealized ion-channel behavior, but they often fail to reproduce the distributed relaxation, power-law impedance, depressed Nyquist arcs, and memory-dependent phase dispersion observed in biological membranes and tissue interfaces.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Objectives<\/jats:title>\n                    <jats:p>This study aims to develop a fractional four-element Windkessel-constant phase framework, denoted BioMem-FWK4\u03b1, for analog simulation and frequency-domain interpretation of biological ion-channel and membrane-like impedance responses.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Design<\/jats:title>\n                    <jats:p>A theoretical, computational, and analog-circuit modeling study was conducted using normalized fractional circuit parameters. The study is intended as a mechanistic modeling framework rather than as a direct experimental validation study.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>The classical four-element Windkessel topology was reformulated by replacing ideal compliance with a constant-phase element of order \u03b1 and by introducing fractional inertial behavior of order \u03b2 and an active\/passive resistance ratio \u03b3. Caputo and Caputo-Fabrizio formulations were compared under explicit zero-initial frequency-domain assumptions. The model was analyzed through transfer functions, Bode plots, Nyquist loci, Nichols diagrams, RC-ladder approximation, sensitivity indicators, and biological interpretation tables.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>The model predicts non-integer gain slopes approaching -20\u03b1 dB per decade, phase plateaus near -90\u03b1 degrees, and depressed Nyquist arcs whose depression increases as \u03b1 decreases. The \u03b3 parameter controls the transition from passive leakage-dominated filtering to active or mixed active-passive regimes, while \u03b2 modifies delayed ionic or kinetic effects. The RC-ladder approximation supports the physical realizability of the fractional element, although biological validation requires future fitting against patch-clamp and bioimpedance datasets.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>BioMem-FWK4\u03b1 provides a compact and interpretable circuit framework for describing memory-rich membrane impedance and ion-channel-like dynamics. It does not replace Hodgkin-Huxley or Markov-state models for detailed nonlinear gating, but complements them by offering a reduced-order frequency-domain and analog-realizable representation of distributed membrane memory. Future work should validate the model using time-resolved patch-clamp, tissue bioimpedance, and voltage-dependent nonlinear parameter identification.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1177\/11795972261484325","type":"journal-article","created":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T09:00:09Z","timestamp":1788166809000},"update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["BioMem-FWK4\u03b1: A Fractional Windkessel\u2013Constant Phase Framework for Analog Simulation and Frequency-Domain Interpretation of Biological Ion Channels"],"prefix":"10.1177","volume":"17","author":[{"given":"Jean Paul","family":"Teuguia","sequence":"first","affiliation":[{"name":"Higher Teacher Training College"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8635-1159","authenticated-orcid":false,"given":"Emmanuel","family":"Fendzi-Donfack","sequence":"additional","affiliation":[{"name":"Higher Teacher Training College"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4049-0716","authenticated-orcid":false,"given":"Wulfran Fendzi","family":"Mbasso","sequence":"additional","affiliation":[{"name":"University of Douala"},{"name":"Saveetha Institute of Medical and Technical Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ambe","family":"Harrison","sequence":"additional","affiliation":[{"name":"Applied Science Private University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8580-9655","authenticated-orcid":false,"given":"Liu","family":"Zhe","sequence":"additional","affiliation":[{"name":"Centre for Research Impact & Outcome, Chitkara University Institute of Engineering and Technology, Chitkara University, Rajpura, Punjab, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zokir","family":"Mamadiyarov","sequence":"additional","affiliation":[{"name":"Termez University of Economics and Service"},{"name":"Mamun University"},{"name":"Alfraganus University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aur\u00e9lien","family":"Kenfack-Jiotsa","sequence":"additional","affiliation":[{"name":"Higher Teacher Training College"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2026,8,31]]},"reference":[{"key":"e_1_3_5_2_2","doi-asserted-by":"publisher","DOI":"10.1113\/jphysiol.1952.sp004764"},{"key":"e_1_3_5_3_2","volume-title":"Ion Channels of Excitable Membranes","author":"Hille B","year":"2001","unstructured":"Hille B. 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