Tolakanahalli R, Tewatia D, Tome W
University of Wisconsin, Madison, WI.
Med Phys. 2012 Jun;39(6Part8):3685-3686. doi: 10.1118/1.4734980.
To demonstrate that Recurrence quantification analysis (RQA) can be used as a quantitative decision making tool to classify patients breathing pattern and select treatment strategy for maneuvering the tumor motion : (a) MIP based treatment (b) 4D treatment using non-linear prediction only (c) 4D treatment non-linear control prediction and breathing control.
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. Recurrence plots enable one to investigate an m-dimensional state space trajectory through a two-dimensional representation of its recurrences where the value of a specific pixel is 1 if the distance between the two corresponding trajectory points is less than a threshold value ε. Important measures calculated are: Recurrence Rate (RR), %Determinism, Divergence, Shannon Entropy, LMean, and Renyi entropy (K2). Time Resolved RQA: By implementing a sliding window design, each of the above calculated parameters is computed multiple times. Alignment of those parameters with the time series reveals details not obvious in the 1 -dimensional time series data. The breathing pattern for seven randomly chosen volunteers were recorded using the RPM system for 15 minutes. Non-linear prediction was performed and the normalized root mean square error (NRMSE) was calculated for each of the volunteer data.
The threshold value ε was chosen such that the Recurrence Rate was equal to 1%. There is a strong correlation of NRMSE with Entropy, Determinism and LMean. Time resolved RR locates strong Unstable Periodic Orbits(UPOs), i.e. patterns of uninterrupted equally spaced diagonal lines.
RQAs could prove to be a very powerful tool for design of personalized treatment regimen. Entropy, Determinism in conjunction with strong UPOs can be used to determine if patients are suitable candidates for prediction and chaos control.
证明递归量化分析（RQA）可作为一种定量决策工具，用于对患者呼吸模式进行分类，并选择控制肿瘤运动的治疗策略：（a）基于最大密度投影（MIP）的治疗；（b）仅使用非线性预测的四维治疗；（c）四维治疗的非线性控制预测和呼吸控制。
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。递归图能够通过其递归的二维表示来研究m维状态空间轨迹，其中如果两个相应轨迹点之间的距离小于阈值ε，则特定像素的值为1。计算的重要指标有：递归率（RR）、确定性百分比、发散度、香农熵、L均值和雷尼熵（K2）。时间分辨RQA：通过实施滑动窗口设计，上述每个计算参数都被多次计算。这些参数与时间序列的对齐揭示了一维时间序列数据中不明显的细节。使用RPM系统记录了七名随机选择的志愿者的15分钟呼吸模式。进行了非线性预测，并为每个志愿者数据计算了归一化均方根误差（NRMSE）。
选择阈值ε使得递归率等于1%。NRMSE与熵、确定性和L均值之间存在很强的相关性。时间分辨RR定位到强不稳定周期轨道（UPOs），即不间断的等间距对角线模式。
RQA可能被证明是设计个性化治疗方案的非常强大的工具。熵、确定性与强UPOs相结合可用于确定患者是否是预测和混沌控制的合适候选者。
