Computational Model-based Statistical Methods in Biomedicine

该项目涉及生物医学应用的数学建模和分析，其目标是从间接和微创测量中检索生物系统结构或功能的相关信息。应用包括脑电图（EEG）和脑磁图（MEG），电阻抗断层扫描（EIT），电神经成像（ENG）和动态PET成像。所有这些问题的特点是描述系统的数学模型的高度复杂性，信号中的显著噪声水平，以及从数据中恢复感兴趣的信息的逆问题的严重不适定性。精心规划的模型约简方法有助于简化模型，但同时也引入了显著的建模误差，因为简化后的模型不再能够捕获数据的所有特征。该项目的目的是开发计算统计方法来克服这些问题。未知量被建模为随机变量，使得从统计角度分析模型缩减误差成为可能。在MEG/EEG应用中，随机建模用于分析和滤除正常大脑活动产生的复杂噪声，这些噪声容易掩盖异常活动（如局灶性癫痫发作）产生的信号。为未知量精心规划的先验模型有助于减少反问题的不适定性，并导致有效的数值方法来估计感兴趣的未知量以及量化估计中的不确定性。研究了一种新的时变滤波方法来处理噪声信号。数学和计算方法旨在提高不同诊断过程的性能：在阻抗断层扫描应用中，目标是能够在不需要乳房活检的情况下，通过乳房接触电极注入弱电流并测量相应的电压，并进一步计算感兴趣组织的电响应，从而识别乳房x线摄影图像中看到的良性和恶性病变。众所周知，癌症组织的特征是异常的电反应。脑电图和脑磁图研究的主要目标是通过测量患者头部外的电场和磁场来帮助定位大脑中的癫痫病灶。这一信息对药物治疗无效的严重癫痫患者的脑部手术计划有很大帮助。动态PET成像用于脑功能的研究，例如，在严重的肝脏状况下改变血液中的铵水平。电神经造影的目的是使用接触微电极以微创的方式读取周围神经内部的电信号。这些数据可以用来帮助病人控制安装在断肢上的假肢机械臂，就好像这条手臂是真正的手臂一样，对神经元指令做出反应。另一个正在研究的令人兴奋的应用是控制慢性疼痛的可能性。

This project concerns the mathematical modeling and analysis of biomedical applications in which the objective is to retrieve pertinent information of the structure or functioning of a biological system from indirect and minimally invasive measurements. The applications include electroencephalography (EEG) and magnetoencephalography (MEG), electrical impedance tomography (EIT), electric neurography (ENG), and dynamical PET imaging. Characteristic for all these problems is the high complexity of the mathematical model describing the system, significant level of noise in the signals, and severe ill-posedness of the inverse problem of recovering the information of interest from the data. Well-planned model reduction methods help to simplify the model, but at the same time a significant modeling error is introduced, as the simplified model can no longer capture all the features of the data. The aim in the project is to develop computational statistical methods to overcome these problems. Unknown quantities are modeled as random variables, making it possible to analyze in statistical terms the model reduction errors. In the MEG/EEG application, stochastic modeling is used to analyze and filter out the complex noise due to normal brain activity that easily masks the signal coming from an abnormal activity such as the onset of focal epileptic seizure. Well-planned prior models for the unknown quantities help to reduce the ill-posedness of the inverse problems, and lead to efficient numerical methods for both estimating the unknowns of interest as well as to quantify the uncertainty in the estimate. Novel time-dependent filtering methods are investigated to deal with noisy signals.The mathematical and computational methodology aims at improving the performance of different diagnostic processes: In the impedance tomography application, the goal is to be able to discern benign and malignant lesions seen in a mammography image without the need of breast biopsy, by injecting weak electric currents through contact electrodes in the breast and measuring the corresponding electric voltages, and by further computing the electric response of the tissue of interest. It is known that cancer tissue is characterized by an abnormal electric response. The main target in EEG and MEG research is to help localizing epileptic foci in the brain by measuring the electric and magnetic fields outside the patient's head. This information helps greatly the brain surgery planning for patients with severe epilepsy that does not respond to medication. Dynamic PET imaging is used in the studies of brain functioning, e.g., under severe liver conditions that change the ammonium level in the blood. Electric neurography aims at reading the electric signals inside a peripheral nerve in a minimally invasive manner using contact microelectrodes. This data can be used to give a patient control of a prosthetic robotic arm mounted on an amputated limb, as if the arm would be a real arm responding to neuronal commands. Another exciting application being investigated is the possibility to control chronic pain.