### Abstract

Purpose: 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.Method and Materials: 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. Results: 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. Conclusions: 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.

Original language | English (US) |
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Pages (from-to) | 3685-3686 |

Number of pages | 2 |

Journal | Medical Physics |

Volume | 39 |

Issue number | 6 |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

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## Cite this

*Medical Physics*,

*39*(6), 3685-3686. https://doi.org/10.1118/1.4734980