Tolakanahalli R, Tewatia D, Tome W
University of Wisconsin, Madison, WI.
Med Phys. 2012 Jun;39(6Part8):3686. doi: 10.1118/1.4734982.
Prediction methods for breathing patterns, which are crucial to deal with system latency in treatments of moving lung tumors using state-space methodologies based on non-linear dynamics are contrasted to linear predictive methods.
In our previous work we established that breathing patterns can be described as a 5-6 dimensional nonlinear, stationary and deterministic system that exhibits sensitive dependence on initial conditions. In this work, nonlinear prediction methods are used to predict the short-term evolution of the respiratory system for 3 patients. Single step and N-point multi step prediction are performed for sampling rates of 5Hz, 10Hz, and 30Hz. We compare the employed nonlinear prediction methods with respect to prediction accuracy to Infinite Impulse Response (IIR) prediction filters. The simplest form of local prediction is finding similar segments of scalar time series data in a higher dimensional embedding space. Hence, we predict the future value x(t)of N-time steps ahead by simply finding the average of nearest neighbor points to the point x(t) in the past and using them to estimate x(t+N), yielding a local average model (LAM). Local linear models (LLM) which are linear autoregressive models that hold only for a region around the target point formed by the nearest neighbor points is combined with a set of linear regularization techniques to solve ill-posed regression problems are also implemented.
For all sampling frequencies, both single step and N-point multi step prediction results obtained using LAM and LLM with regularization methods are better than IIR prediction filters for the selected sample patients.
The use of non-linear prediction methods for predicting the breathing pattern of lung cancer patients may lead to improved, robust and accurate long-term prediction to account for system latencies.
将基于非线性动力学的状态空间方法用于移动性肺肿瘤治疗中处理系统延迟的呼吸模式预测方法，与线性预测方法进行对比。
在我们之前的工作中，我们确定呼吸模式可被描述为一个5 - 6维的非线性、平稳且确定性的系统，该系统对初始条件表现出敏感依赖性。在这项工作中，使用非线性预测方法对3名患者的呼吸系统短期演变进行预测。针对5Hz、10Hz和30Hz的采样率进行单步和N点多步预测。我们将所采用的非线性预测方法在预测准确性方面与无限脉冲响应（IIR）预测滤波器进行比较。局部预测的最简单形式是在更高维嵌入空间中找到标量时间序列数据的相似段。因此，我们通过简单地找到过去点x(t)的最近邻点的平均值并使用它们来估计x(t + N)，从而预测未来N个时间步的未来值x(t)，得到一个局部平均模型（LAM）。还实现了局部线性模型（LLM），它是仅在由最近邻点形成的目标点周围区域成立的线性自回归模型，并与一组线性正则化技术相结合以解决不适定回归问题。
对于所有采样频率，使用LAM和带有正则化方法的LLM获得的单步和N点多步预测结果，对于所选样本患者而言，均优于IIR预测滤波器。
使用非线性预测方法来预测肺癌患者的呼吸模式，可能会带来改进的、稳健且准确的长期预测，以应对系统延迟。
