CAREER: Embracing Complexity: A Fractal Calculus Approach to the Modeling and Optimization of Medical Cyber-Physical Systems

这项跨学科的研究提出了一种针对患者的成本节约方法，以设计和优化医疗保健网络物理系统(HCPS)。HCPS基于传感器计算患者的生理状态，通过从家庭到医院的网络传递该信息以量化风险指数，实时发出关键医疗干预的需要的信号，并控制重要的健康信号(例如，心率、血糖)。在HCPS范式下提出的研究将把人体视为一个复杂的系统。它将需要开发数学模型来捕捉生理过程的时间依赖性和分形性行为，并设计医疗器械的生活质量(QOL)控制策略。这项研究将促进对生理过程、药物治疗、压力水平和生活方式之间的相关性的理解。到目前为止，在医疗器械和人工器官的设计中还没有考虑到生理过程的复杂的相互依存性、变异性和个体特征。现有的数学方法依赖于简化论和马尔可夫假设。这项研究项目将通过捕捉高度动态网络中生理过程的相互依赖和分形特征来重新思考医疗保健网络物理系统设计的理论基础。为了建立HCPS的理论基础，将遵循三个步骤：(I)构建一个多尺度非平衡统计物理启发的患者建模框架，该框架捕捉生理过程的时间依赖性、非高斯行为、相互依赖和多重分形行为；(Ii)为动态复杂网络开发自适应的患者特定和生理感知(多重分形)闭环控制算法；(Iii)设计考虑生物和技术约束的HCPS联网组件的算法和方法。这项研究将对慢性病的早期发现和治疗做出重大贡献。模型和可实施的算法，既可以预测生理动态，也可以评估急性和慢性疾病的风险，将是以患者为中心的医疗保健的有价值的工具。这种对生理复杂性的深入数学分析促进了具有医疗保健应用的变革性多模式和多尺度的CPS设计方法。该项目不仅解决了CPS目前的科学和技术差距，而且还可以促进相关领域的新的研究方向，如相互依赖的网络的研究，这对理解动态平衡和疾病以及复杂系统的研究和控制具有重要意义。根据这一新提出的范例设计的网络-物理系统将产生重要的社会和经济影响，包括改善生活质量和减少因慢性病造成的生产率损失。该项目将为研究生、本科生和K-12学生提供跨学科培训。PI将把研究成果整合到他在南加州大学的课程中，并通过项目网站广泛提供。此外，通过让大学生和K-12学生参加社区外展活动，提高人们对健康监测的重要作用的认识，PI将加强公民参与。

This cross-disciplinary research proposes a patient-specific cost-saving approach to the design and optimization of healthcare cyber-physical systems (HCPS). The HCPS computes the patient's physiological state based on sensors, communicates this information via a network from home to hospital for quantifying risk indices, signals the need for critical medical intervention in real time, and controls vital health signals (e.g., cardiac rhythm, blood glucose). The research proposed under the HCPS paradigm will treat the human body as a complex system. It will entail the development of mathematical models that capture the time-dependence and fractal behavior of physiological processes and the design of quality-of-life (QoL) control strategies for medical devices. The research will advance the understanding of the correlations between physiological processes, drug treatment, stress level and lifestyle. To date, the complex interdependence, variability and individual characteristics of physiological processes have not been taken into account in the design of medical devices and artificial organs. The existing mathematical approaches rely on reductionist and Markovian assumptions. This research project will rethink the theoretical foundations for the design of healthcare cyber-physical systems by capturing the interdependencies and fractal characteristics of physiological processes within a highly dynamic network. To establish the theoretical foundations of HCPS, a three-step approach will be followed: (i) construct a multi-scale non-equilibrium statistical physics inspired framework for patient modeling that captures the time dependence, non-Gaussian behavior, interdependencies and multi-fractal behavior of physiological processes; (ii) develop adaptive patient-specific and physiology-aware (multi-fractal) close-loop control algorithms for dynamic complex networks; (iii) design algorithms and methodologies for the HCPS networked components that account for biological and technological constraints. This research will significantly contribute to early chronic disease detection and treatment. Models and implementable algorithms, which can both predict physiological dynamics and assess the risk of acute and chronic diseases, will be valuable instruments for patient-centered healthcare. This in-depth mathematical analysis of physiological complexity facilitates a transformative multimodal and multi-scale approach to CPS design with healthcare applications.The project not only addresses the current scientific and technological gap in CPS, but can also foster new research directions in related fields such as the study of interdependent networks with implications for understanding homeostasis and diseases and the study and control of complex systems. The cyber-physical systems designed under this newly proposed paradigm will have vital social and economic implications, including the improvement of QoL and the reduction of lost productivity rates due to chronic diseases. The project will offer interdisciplinary training for graduate, undergraduate and K-12 students. The PI will integrate the research results within his courses at University of Southern California and make them widely available through the project website. Moreover, the PI will enhance civic engagement by involving college and K-12 students in community outreach activities that will raise awareness of the important role of health monitoring.