Alzheimer’s disease is a complex, multi-factorial, and multi-parametric neurodegenerative etiology. Mathematical models can help understand such a complex problem by providing a way to explore and conceptualize principles, merging biological knowledge with experimental data into a model amenable to simulation and external validation, all without the need for extensive clinical trials. We performed a scoping review of mathematical models describing the onset and evolution of Alzheimer’s disease as a result of biophysical factors following the PRISMA standard. Our search strategy applied to the PubMed database yielded 846 entries. After using our exclusion criteria, only 17 studies remained from which we extracted data, which focused on three aspects of mathematical modeling: how authors addressed continuous time (since even when the measurements are punctual, the biological processes underlying Alzheimer’s disease evolve continuously), how models were solved, and how the high dimensionality and non-linearity of models were managed. Most articles modeled Alzheimer’s disease at the cellular level, operating on a short time scale (e.g., minutes or hours), i.e., the micro view (12/17); the rest considered regional or brain-level processes with longer timescales (e.g., years or decades) (the macro view). Most papers were concerned primarily with amyloid beta (n = 8), few described both amyloid beta and tau proteins (n = 3), while some considered more than these two factors (n = 6). Models used partial differential equations (n = 3), ordinary differential equations (n = 7), and both partial differential equations and ordinary differential equations (n = 3). Some did not specify their mathematical formalism (n = 4). Sensitivity analyses were performed in only a small number of papers (4/17). Overall, we found that only two studies could be considered valid in terms of parameters and conclusions, and two more were partially valid. This puts the majority (n = 13) as being either invalid or with insufficient information to ascertain their status. This was the main finding of our paper, in that serious shortcomings make their results invalid or non-reproducible. These shortcomings come from insufficient methodological description, poor calibration, or the impossibility of experimentally validating or calibrating the model. Those shortcomings should be addressed by future authors to unlock the usefulness of mathematical models in Alzheimer’s disease.
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Dr. David Lowemann, M.Sc, Ph.D., is a co-founder of the Institute for the Future of Human Potential, where he leads the charge in pioneering Self-Enhancement Science for the Success of Society. With a keen interest in exploring the untapped potential of the human mind, Dr. Lowemann has dedicated his career to pushing the boundaries of human capabilities and understanding.
Armed with a Master of Science degree and a Ph.D. in his field, Dr. Lowemann has consistently been at the forefront of research and innovation, delving into ways to optimize human performance, cognition, and overall well-being. His work at the Institute revolves around a profound commitment to harnessing cutting-edge science and technology to help individuals lead more fulfilling and intelligent lives.
Dr. Lowemann’s influence extends to the educational platform BetterSmarter.me, where he shares his insights, findings, and personal development strategies with a broader audience. His ongoing mission is shaping the way we perceive and leverage the vast capacities of the human mind, offering invaluable contributions to society’s overall success and collective well-being.