Название: Simulating the Brain: A Four-Step Method Using Ordinary Differential Equations and PythonАвтор: Daniele Caligiore, Samuele Carli
Издательство: Springer
Год: 2025
Страниц: 209
Язык: английский
Формат: pdf (true), epub
Размер: 76.7 MB
This book presents a new methodology to develop system-level brain models using ordinary differential equations (ODE), which are to be solved and analyzed through simple Python scripts. Computer simulations of this kind of models allow the study of healthy and damaged brain functions, the discovery of new neural pathways that may be crucial for the emergence of pathologies, and to simulate the effects of possible new therapies acting on brain actors which are difficult to investigate in traditional research.
The methodology consists of four steps: (i) design the model architecture which represents the interactions between different brain areas; (ii) write the ODE system which are implied by the model; (iii) build a Python script that correctly solves the equations; (iv) optimize the free model parameters using genetic algorithms or other techniques to obtain one or more model instances that reproduce the target investigated behavior.
This book is for all people who want to learn how to use Python and ODE to simulate brain functions regardless of their backgrounds. While rigorous mathematical proofs of many aspects of the arguments discussed are out of the scope of this work and are therefore omitted, the most important concepts necessary for the critical judgment and self-assessment of the practitioner’s work are exposed in a simplified, readily applicable form, with extensive references for the adventurous reader to explore.
Python is widely regarded as one of the best languages for implementing scientific simulation code due to its simplicity, readability, and extensive ecosystem of libraries. Its easy-to-understand syntax reduces the complexity of translating mathematical models into code, allowing scientists to focus on problem-solving rather than programming intricacies. Additionally, Python’s robust libraries, such as NumPy for numerical computations, SciPy for advanced scientific calculations, and Matplotlib for data visualization, provide powerful tools for developing and analyzing simulations efficiently. The strong community support and constant development of new packages further enhance Python’s capabilities, making it an indispensable tool for scientific research and simulation. There are (rare) cases where Python may not be performant enough for the task at hand, but it is easy to interface and extend Python programs with lower level languages like C, C++ and Rust; performance critical parts of the any program can be implemented in such languages while Python glues everything together. Python is usually a great first choice to carry out any of the tasks needed by a scientific project.
The book is a self-consistent textbook containing all pieces necessary to learn from scratch: from the essential mathematical and computing tools to the knowledge necessary to design, simulate, visualize, and interpret brain models. These skills are acquired through several hands-on examples explained step-by-step. One important and distinctive aspect of the book is that, beside the theory, it provides the necessary contexts and practical examples which are key to the correct application of the proposed methodology.
This textbook is a comprehensive resource, providing everything needed to learn from the ground up. It covers essential mathematical concepts—ranging from foundational topics for beginners to insights on advanced subjects for more experienced readers—as well as fundamental computing and collaboration tools indispensable for interdisciplinary, team-based research. Additionally, it introduces the basics of Python programming and equips readers with the skills to design, simulate, visualize, and interpret models of the brain and other complex systems. These abilities are honed through numerous hands-on examples, explained step-by-step.
- Proposes a four steps groundbreaking methodology to build system-level brain models using Python and ODE
- Provides necessary contexts and practical examples which are key to the correct application of the proposed methodology
- Shows how to simulate with the computer healthy and damaged brains functions and the effects of possible new therapies
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