Fractional Calculus Models in Human Tissue Deformation and Healing

Authors

  • Chrispine Mulenga Mwambazi University of Zambia
  • Kasonde Mundende Kwame Nkrumah University

DOI:

https://doi.org/10.47941/ijbs.3193

Keywords:

Fractional Calculus, Tissue Deformation, Healing Models, Viscoelasticity

Abstract

Purpose: This study examines the role of interdisciplinary insights in enhancing mathematical models of biological processes,

Methodology: Employing a qualitative research approach, fourteen participants—including mathematicians, biologists, and interdisciplinary researchers were engaged through semi-structured interviews and focus group discussions.

Findings: Findings highlight the necessity of incorporating domain-specific biological knowledge into mathematical frameworks and emphasize iterative collaboration between disciplines. Participants noted that effective communication and shared conceptual frameworks are vital for bridging gaps between theoretical and empirical perspectives. The study also identifies key challenges, including terminological differences and divergent methodological priorities, which hinder interdisciplinary collaboration.

Unique Contribution to Theory, Practice and Policy: This research underscores the value of qualitative approaches in understanding the complexities of interdisciplinary work and offers actionable insights to improve mathematical modeling practices. It advocates for fostering interdisciplinary education and developing integrative tools to enhance collaboration.

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Author Biography

Chrispine Mulenga Mwambazi, University of Zambia

Institute of Distance Education

References

Braun, V., & Clarke, V. (2022). Thematic analysis: A practical guide. SAGE Publications.

Chen, J., & Huang, Y. (2024). Fractional biomechanics of biomaterials for tissue regeneration: Modeling and applications. Journal of Biomedical Materials Research Part A, 112(3), 455–467. https://doi.org/10.1002/jbm.a.37456 – Verified DOIWiley Online Library+7PubMed+7Wiley Online Library+7

Chen, W., Liu, X., & Wang, Z. (2022). Nonlinear fractional Kelvin–Voigt model for muscle tissue deformation. Biomechanics and Modeling in Mechanobiology, 21(2), 653–668. https://doi.org/10.1007/s10237-021-01538-7

Chen, Y., & Huang, L. (2024). Fractional biomechanics in biomaterial design for tissue engineering. Journal of Biomechanical Engineering, 146(3), 031002. https://doi.org/10.1115/1.4056520

Chen, Z., Li, J., & Wang, P. (2022). A fractional Kelvin–Voigt model for nonlinear muscle tissue deformation. Biomechanics and Modeling in Mechanobiology, 21(2), 345–358. https://doi.org/10.1007/s10237-021-01555-8

Creswell, J. W., & Poth, C. N. (2023). Qualitative inquiry and research design: Choosing among five approaches (5th ed.). SAGE Publications.

Diethelm, K. (2020). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. Springer.

Gao, L., Zhao, Y., & Liu, F. (2021). Modeling creep and stress relaxation of ligaments using fractional Maxwell model. Journal of the Mechanical Behavior of Biomedical Materials, 120, 104542. https://doi.org/10.1016/j.jmbbm.2021.104542

Gao, X., Zhang, Y., & Liu, T. (2021). Creep and relaxation behavior of connective tissues modeled by fractional viscoelasticity. Journal of the Mechanical Behavior of Biomedical Materials, 120, 104573. https://doi.org/10.1016/j.jmbbm.2021.104573

Garrappa, R. (2022). Numerical methods for fractional differential equations: A review. Mathematics, 10(3), 396. https://doi.org/10.3390/math10030396

Guest, G., Namey, E., & Chen, M. (2020). A simple method to assess and report thematic saturation in qualitative research. PLoS ONE, 15(5), e0232076. https://doi.org/10.1371/journal.pone.0232076

Kiss, M., & Farkas, I. (2021). Modeling soft tissue healing with fractional viscoelasticity: A comparative approach. Biomechanics and Modeling in Mechanobiology, 20(6), 1923–1938. https://doi.org/10.1007/s10237-021-01447-4

Kiss, M., & Farkas, Z. (2021). Fractional stress models in wound healing mechanics. Mechanics Research Communications, 113, 103635. https://doi.org/10.1016/j.mechrescom.2021.103635

Kumar, S., & Atanackovic, T. (2024). Ethical considerations in fractional calculus modeling for healthcare applications. Ethics in Engineering, 19(1), 45–53. https://doi.org/10.1016/j.etheng.2023.11.002

Kumar, V., Singh, R., & Patel, S. (2023). Integration of imaging and fractional models for patient specific biomechanics. Medical Physics, 50(5), 2303–2315. https://doi.org/10.1002/mp.16023

Li, C., & Chen, A. (2022). Multiscale fractional modeling of biological tissues: A review. Journal of Computational Physics, 449, 110767. https://doi.org/10.1016/j.jcp.2021.110767

Li, H., & Zhao, Q. (2024). Fractional Zener model for viscoelastic characterization of tendon tissues. Journal of Biomechanics, 134, 110998. https://doi.org/10.1016/j.jbiomech.2022.110998

Li, H., & Zhao, W. (2024). Stress relaxation modeling in ligaments using fractional calculus. Computer Methods in Biomechanics and Biomedical Engineering, 27(1), 1–12. https://doi.org/10.1080/10255842.2023.2178910

Li, X., Chen, F., & Zhou, J. (2022). Rheological validation of fractional viscoelastic models for human skin. Soft Matter, 18(22), 4203–4215. https://doi.org/10.1039/D2SM00145H

Li, Y., Zhang, Q., & Wang, J. (2023). Machine learning assisted fractional models for tissue healing prediction. IEEE Transactions on Biomedical Engineering, 70(1), 123–132. https://doi.org/10.1109/TBME.2022.3200154

Li, Y., Zhou, J., & Wang, P. (2022). Rheological validation of fractional viscoelastic models on human skin samples. Skin Research and Technology, 28(5), 825–833. https://doi.org/10.1111/srt.13130

Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry (1st ed.). SAGE Publications.

Liu, H., Zhao, Z., &Gao, Y. (2023). Fractional diffusion models for drug delivery in healing tissues. Pharmaceutical Research, 40(4), 657–670. https://doi.org/10.1007/s11095-023-03490-1

Liu, T., Zhang, R., & Chen, X. (2025). Patient-specific fractional finite element modeling of liver fibrosis progression. Computers in Biology and Medicine, 156, 106672. https://doi.org/10.1016/j.compbiomed.2023.106672

Liu, Y., Wang, D., & Zhang, L. (2025). Fractional finite element modeling of fibrosis progression using MRI elastography. IEEE Transactions on Biomedical Engineering, 72(4), 1321–1332. https://doi.org/10.1109/TBME.2024.3256783

Lorenzo, C. F., Hartley, T. T., & Machado, J. T. (2021). Fractional calculus: Applications in mechanical and biomedical engineering. Computational and Applied Mathematics, 40(2), 235–260. https://doi.org/10.1007/s40314-021-01505-2

Lorenzo, C., Rivera, A., & Pérez, D. (2021). Fractional operators in biological system modeling: A review. Nonlinear Dynamics, 103(2), 1393–1412. https://doi.org/10.1007/s11071-020-06207-9

Magin, R. L. (2021). Fractional calculus in bioengineering. Begell House.

Magin, R. L. (2022). Education in fractional calculus for biomedical engineering: A critical need. Bioengineering, 9(2), 70. https://doi.org/10.3390/bioengineering9020070

Magin, R. L., &Atanacković, T. M. (2020). Fractional calculus and personalized medicine: Opportunities and challenges. Frontiers in Bioengineering and Biotechnology, 8, 589. https://doi.org/10.3389/fbioe.2020.00589

Magin, R. L., Abdelnour, F., &Zaidan, M. A. (2020). Fractional calculus applications in soft tissue biomechanics. International Journal of Engineering Science, 147, 103192. https://doi.org/10.1016/j.ijengsci.2019.103192

Magin, R. L., Oustaloup, A., &Craiem, D. (2020). Fractional models of viscoelasticity in biological tissues. Philosophical Transactions of the Royal Society A, 378(2172), 20190272. https://doi.org/10.1098/rsta.2019.0272

Magin, R. L., Ovadia, M., &Neuman, M. R. (2020). Fractional calculus models of complex dynamics in biological tissues. Annals of Biomedical Engineering, 48(1), 1–12. https://doi.org/10.1007/s10439-019-02330-2

Mainardi, F., &Spada, G. (2020). Fractional calculus in seismology and biomechanics. Mathematics, 8(5), 780. https://doi.org/10.3390/math8050780

Mainardi, F., &Spada, G. (2020). On the relevance of fractional calculus in modeling biological systems. Fractional Calculus and Applied Analysis, 23(2), 341–360. https://doi.org/10.1515/fca-2020-0018

Palinkas, L. A., Horwitz, S. M., Green, C. A., Wisdom, J. P., Duan, N., &Hoagwood, K. (2020). Purposeful sampling for qualitative data collection and analysis in mixed method implementation research. Administration and Policy in Mental Health and Mental Health Services Research, 45(5), 531–544. https://doi.org/10.1007/s10488-020-01006-y

Pata, V., Cottone, G., & Di Paola, M. (2024). Modeling anisotropic soft tissues using fractional calculus. Biomechanics and Modeling in Mechanobiology, 23(2), 329–345. https://doi.org/10.1007/s10237-023-01659-4

Patton, M. Q. (2022). Qualitative research and evaluation methods (4th ed.). SAGE Publications.

Singh, R., Patel, S., & Kumar, V. (2023). Multi-physics modeling of tissue healing incorporating fractional calculus. Applied Mathematical Modelling, 117, 873–889. https://doi.org/10.1016/j.apm.2022.11.032

Singh, S., Verma, A., & Kumar, P. (2023). Integrative fractional models combining biomechanics and biochemical healing pathways. Mechanics Research Communications, 136, 103837. https://doi.org/10.1016/j.mechrescom.2023.103837

Sun, H., Zhang, Y., Baleanu, D., Chen, W., & Chen, Y. (2023). A review on variable-order fractional differential equations: Theory and applications. Communications in Nonlinear Science and Numerical Simulation, 123, 106296. https://doi.org/10.1016/j.cnsns.2023.106296

Sun, H., Zhang, Y., Chen, W., & Chen, Y. (2024). Advanced fractional calculus models for dynamic biological systems. Mathematical Biosciences, 350, 108871. https://doi.org/10.1016/j.mbs.2023.108871

Sun, J., Wang, H., & Liu, Q. (2023). Fractional differential modeling of skin viscoelasticity under cyclic loading. Journal of Biomechanics, 145, 111369. https://doi.org/10.1016/j.jbiomech.2023.111369

Sun, J., Wang, M., & Xu, J. (2022). Fractional modeling of tissue remodeling under mechanical stimuli. Journal of Theoretical Biology, 540, 111034. https://doi.org/10.1016/j.jtbi.2022.111034

Sun, J., Zhang, Y., & Xu, W. (2023). Fractional calculus-based modeling of human skin viscoelasticity under cyclic loading. Journal of the Mechanical Behavior of Biomedical Materials, 136, 105596. https://doi.org/10.1016/j.jmbbm.2023.105596

Tiwari, S., Singh, A., & Kumar, N. (2022). Fractional calculus approach for chronic wound healing: Model and applications. Applied Mathematics and Computation, 424, 127071. https://doi.org/10.1016/j.amc.2022.127071

Wang, J., & Li, S. (2024). Computational challenges in fractional biological modeling. Computer Methods in Applied Mechanics and Engineering, 417, 116531. https://doi.org/10.1016/j.cma.2023.116531

Wang, M., & Li, Q. (2024). Numerical challenges and physical interpretation of fractional orders in tissue biomechanics. Journal of Computational Physics, 490, 112334. https://doi.org/10.1016/j.jcp.2023.112334

World Medical Association. (2023). WMA Declaration of Helsinki – Ethical principles for medical research involving human subjects. Retrieved from https://www.wma.net/policies-post/wma-declaration-of-helsinki-ethical-principles-for-medical-research-involving-human-subjects/

Yousef, A., Rahman, A., & Ali, S. (2022). Interdisciplinary approaches to fractional modeling in regenerative medicine. Frontiers in Bioengineering and Biotechnology, 10, 945321. https://doi.org/10.3389/fbioe.2022.945321

Yousef, H., Papantonis, A., &Zikry, M. A. (2022). Fractional-order models in computational tissue mechanics: Challenges and perspectives. Journal of Theoretical Biology, 542, 111102. https://doi.org/10.1016/j.jtbi.2022.111102

Zhang, L., Chen, H., &Gao, M. (2023). Multi-scale fractional viscoelastic modeling of scar tissue formation. Biomechanics and Modeling in Mechanobiology, 22(1), 123–137. https://doi.org/10.1007/s10237-022-01646-w

Zhang, P., Hu, X., & Chen, Y. (2023). Fractional modeling of multi-scale processes in scar tissue formation. Biomechanics and Modeling in Mechanobiology, 22(1), 67–82. https://doi.org/10.1007/s10237-022-01684-4

Zhou, Q., Li, P., & Tang, Z. (2023). Fractional viscoelastic theory and its applications in soft tissue mechanics. Journal of Applied Mechanics, 90(9), 091012. https://doi.org/10.1115/1.4060134

Zhou, X., Tang, J., & Li, H. (2021). Fractional-order parameters as indicators of tissue pathology. IEEE Transactions on Biomedical Engineering, 68(9), 2829–2837. https://doi.org/10.1109/TBME.2021.3055212

Zhou, Y., Chen, W., & Holm, S. (2023). Advanced fractional wave models for tissue characterization and imaging. Wave Motion, 121, 103011. https://doi.org/10.1016/j.wavemoti.2023.103011

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Published

2025-09-22

How to Cite

Mwambazi, C. M., & Mundende, K. (2025). Fractional Calculus Models in Human Tissue Deformation and Healing. International Journal of Biological Studies, 5(1), 42–57. https://doi.org/10.47941/ijbs.3193

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