Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems

约束生物力学多体系统双层优化控制脑瘫诊断和治疗设计的数值方法

• 批准号: 314150787
• 负责人: Professor Dr. Hans Georg Bock
• 金额: --
• 依托单位: Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/314150787?language=en
• 关键词: Numerical; Methods; Diagnosis; Therapy; Design

This project emerged from a long-standing collaboration with the MotionLab of the Heidelberg University Hospital and intends to develop a mathematical model for the human gait and numerical methods for the solution of inverse and robustified optimal control problems to support a detailed diagnosis and a subsequent systematic planning of a therapy for patients with cerebral palsy (CP). CP is a movement disorder, caused by abnormal development of the brain in an early infancy, that effects muscle coordination, leads to deformed bones and can be characterized by a crouched gait. As the basis of this model a constraint biomechanical multi-body system is developed. As the solution of the variational problem with state constraints already the differential equations exhibit non-smooth and discontinuous MPEC type switching dynamics. The gait of the patient is modeled as a solution of an optimal control problem characterizing the patient attempts to optimize criteria like efficiency or stability. Two different bilevel optimal control problems, or infinite MPECs, and their numerical solution are the core of the project. An inverse optimal control problem calibrates the OCP model to measured marker data of the patient's gait, thus individualizing the model. Together with a sensitivity analysis this provides the physician with much more detailed information for a diagnosis of causes of the disorder. In a second stage, this individualized patient model is then used to systematically plan - and optimize - a therapy by surgical intervention or physiotherapy. Here, the OCP must be robustified as a worst case optimization to account for uncertainties in the parameters and inexact realizations of the controls. Numerous mathematical challenges need to be answered to arrive at an efficient solution for this non-smooth and complementarity based problems: effective ways to deal with a lack of constraint qualification, structure exploitation in the discretized multi-level problems and generation of higher-order derivatives, new strategies for globalizing convergence, techniques to avoid weak stationary points and sensitivity analysis of non-smooth optimal control solutions. A part not to be underestimated is an adequate translation of the mathematical results back into the world of the physician, e.g., by adequate visualization tools, supporting diagnosis as well as systematic therapy planning.

该项目源于与海德堡大学医院MotionLab的长期合作，旨在开发人类步态的数学模型和数值方法，用于解决逆向和鲁棒最优控制问题，以支持脑瘫患者的详细诊断和随后的系统治疗计划。CP是一种运动障碍，由婴儿早期大脑发育异常引起，影响肌肉协调，导致骨骼变形，并可表现为蹲伏步态。作为该模型的基础，建立了约束生物力学多体系统。作为具有状态约束的变分问题的解，微分方程已经表现出非光滑和不连续的MPEC型切换动力学。患者的步态被建模为表征患者试图优化效率或稳定性等标准的最优控制问题的解决方案。两个不同的两层最优控制问题，或无限的MPEC，和他们的数值解是该项目的核心。逆最优控制问题将OCP模型校准到患者步态的测量标记数据，从而使模型个性化。与敏感性分析一起，这为医生提供了更详细的信息，用于诊断疾病的原因。在第二阶段，这种个性化的患者模型然后被用于系统地计划-和优化-通过手术干预或物理治疗的治疗。在这里，OCP必须作为最坏情况下的优化鲁棒，以考虑参数的不确定性和控制的不精确实现。众多的数学挑战需要回答，以达到一个有效的解决方案，这个非光滑和互补性为基础的问题：有效的方法来处理缺乏约束资格，结构开发的离散化多层次的问题和生成高阶导数，新的战略，全球化收敛，技术，以避免弱不动点和灵敏度分析的非光滑最优控制解决方案。不可低估的一部分是将数学结果充分翻译回医生的世界，例如，通过适当的可视化工具，支持诊断以及系统的治疗计划。