Lung Transplant Surgery with the ψ–Hamzah Model: A Fractal–Fractional Paradigm for Optimizing Outcomes in End-Stage Pulmonary Disease.

All Articles are Available: Orcid ID: https://orcid.org/my-orcid?orcid=0009-0009-3175-8563 Science Open ID: https://www.scienceopen.com/user/2c98a8bc-b8bb-49b3-9c91-2f2986a7e16e Safe Creative register the work titled "The Theory of Intelligent Evolution, the Hamzah Equation, and the Quantum Civilisation". Safe Creative registration #2504151474836. . Lung transplantation represents the final therapeutic option for patients with end-stage pulmonary diseases such as idiopathic pulmonary fibrosis, chronic obstructive pulmonary disease (COPD), pulmonary hypertension, and cystic fibrosis. While advances in surgical techniques, immunosuppressive regimens, and perioperative care have significantly improved short-term outcomes, long-term prognosis remains limited. Graft rejection, chronic lung allograft dysfunction (CLAD), infection, ischemia-reperfusion injury, and systemic immunosuppression-related complications continue to impose substantial morbidity and mortality. The average 5-year survival rate post-lung transplantation is barely 50–55%, significantly lower compared to other solid organ transplants. This reality underscores the urgent need for a radical rethinking of lung transplant medicine. The ψ–Hamzah model introduces such a paradigm shift. Unlike conventional linear approaches, this framework integrates fractional calculus, fractal geometry, memory-embedded functions, and complex integral equations to accurately capture the non-linear and multi-scale dynamics of lung physiology, immunology, and surgical outcomes. By modeling immune tolerance, vascular adaptation, and graft-host interactions through fractional derivatives, the ψ–Hamzah framework enables precise simulation of transplant outcomes at both cellular and systemic levels. Importantly, it incorporates biological memory effects, which are critical in predicting long-term immune responses, graft adaptation, and chronic rejection risks. Within this framework, two breakthrough innovations are proposed: ψ–Hamzah ImmunoVax – a nanovaccine designed to ...